Kra, Irwin
Overview
Works:  52 works in 277 publications in 2 languages and 5,667 library holdings 

Genres:  Conference papers and proceedings Biography 
Roles:  Editor, Author, Other, Contributor, htt 
Classifications:  QA333, 515.9 
Publication Timeline
.
Most widely held works by
Irwin Kra
Complex analysis : in the spirit of Lipman Bers by
Jane Gilman(
)
36 editions published between 2007 and 2013 in English and held by 1,154 WorldCat member libraries worldwide
"This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complexvalued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and threemanifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education of every practicing mathematician, and it will also be of interest to computer scientists, physicists, and engineers." "The book covers most, if not all, of the material contained in Bers's courses on first year complex analysis. In addition, topics of current interest such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis are explored."Jacket
36 editions published between 2007 and 2013 in English and held by 1,154 WorldCat member libraries worldwide
"This book is intended for a graduate course on complex analysis, also known as function theory. The main focus is the theory of complexvalued functions of a single complex variable. This theory is a prerequisite for the study of many current and rapidly developing areas of mathematics including the theory of several and infinitely many complex variables, the theory of groups, hyperbolic geometry and threemanifolds, and number theory. Complex analysis has connections and applications to many other subjects in mathematics and to other sciences. It is an area where the classic and the modern techniques meet and benefit from each other. This material should be part of the education of every practicing mathematician, and it will also be of interest to computer scientists, physicists, and engineers." "The book covers most, if not all, of the material contained in Bers's courses on first year complex analysis. In addition, topics of current interest such as zeros of holomorphic functions and the connection between hyperbolic geometry and complex analysis are explored."Jacket
Riemann surfaces by
Hershel M Farkas(
Book
)
29 editions published between 1979 and 2003 in English and Undetermined and held by 1,052 WorldCat member libraries worldwide
This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case. Basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the Abelian varities associated with these surfaces. Topics covered include existence of meromorphic functions, the Riemann Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented. Alternate proofs for the most important results are included, showing the diversity of approaches to the subject. For this new edition, the material has been brought up todate, and erros have been corrected. The book should be of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics
29 editions published between 1979 and 2003 in English and Undetermined and held by 1,052 WorldCat member libraries worldwide
This text covers Riemann surface theory from elementary aspects to the fontiers of current research. Open and closed surfaces are treated with emphasis on the compact case. Basic tools are developed to describe the analytic, geometric, and algebraic properties of Riemann surfaces and the Abelian varities associated with these surfaces. Topics covered include existence of meromorphic functions, the Riemann Roch theorem, Abel's theorem, the Jacobi inversion problem, Noether's theorem, and the Riemann vanishing theorem. A complete treatment of the uniformization of Riemann sufaces via Fuchsian groups, including branched coverings, is presented. Alternate proofs for the most important results are included, showing the diversity of approaches to the subject. For this new edition, the material has been brought up todate, and erros have been corrected. The book should be of interest not only to pure mathematicians, but also to physicists interested in string theory and related topics
Riemann surfaces and related topics : proceedings of the 1978 Stony Brook conference by Conference on Riemann Surfaces and Related Topics(
Book
)
20 editions published between 1980 and 1981 in English and held by 680 WorldCat member libraries worldwide
20 editions published between 1980 and 1981 in English and held by 680 WorldCat member libraries worldwide
A crash course on Kleinian groups; lectures given at a special session at the January 1974 meeting of the American Mathematical
Society at San Francisco by
American Mathematical Society(
Book
)
22 editions published between 1974 and 2006 in English and held by 533 WorldCat member libraries worldwide
A little girl discovers that all things have an opposite
22 editions published between 1974 and 2006 in English and held by 533 WorldCat member libraries worldwide
A little girl discovers that all things have an opposite
Automorphic forms and Kleinian groups by
Irwin Kra(
Book
)
20 editions published between 1972 and 1975 in 3 languages and held by 399 WorldCat member libraries worldwide
20 editions published between 1972 and 1975 in 3 languages and held by 399 WorldCat member libraries worldwide
Hilbert's fourth problem by
A. V Pogorelov(
Book
)
6 editions published in 1979 in English and held by 361 WorldCat member libraries worldwide
6 editions published in 1979 in English and held by 361 WorldCat member libraries worldwide
Theta constants, Riemann surfaces, and the modular group : an introduction with applications to uniformization theorems, partition
identities, and combinatorial number theory by
Hershel M Farkas(
Book
)
16 editions published between 2001 and 2012 in English and held by 322 WorldCat member libraries worldwide
There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for numbertheoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova. Theta functions are also classically connected with Riemann surfaces and with the modular group $\Gamma = \mathrm{PSL}(2,\mathbb{Z})$, which provide another path for insights into number theory. Farkas and Kra, wellknown masters of the theory of Riemann surfaces and the analysis of theta functions, uncover here interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. For instance, the authors use this approach to derive congruences discovered by Ramanujan for the partition function, with the main ingredient being the construction of the same function in more than one way. The authors also obtain a variant on Jacobi's famous result on the number of ways that an integer can be represented as a sum of four squares, replacing the squares by triangular numbers and, in the process, obtaining a cleaner result. The recent trend of applying the ideas and methods of algebraic geometry to the study of theta functions and number theory has resulted in great advances in the area. However, the authors choose to stay with the classical point of view. As a result, their statements and proofs are very concrete. In this book the mathematician familiar with the algebraic geometry approach to theta functions and number theory will find many interesting ideas as well as detailed explanations and derivations of new and old results. Highlights of the book include systematic studies of theta constant identities, uniformizations of surfaces represented by subgroups of the modular group, partition identities, and Fourier coefficients of automorphic functions. Prerequisites are a solid understanding of complex analysis, some familiarity with Riemann surfaces, Fuchsian groups, and elliptic functions, and an interest in number theory. The book contains summaries of some of the required material, particularly for theta functions and theta constants. Readers will find here a careful exposition of a classical point of view of analysis and number theory. Presented are numerous examples plus suggestions for researchlevel problems. The text is suitable for a graduate course or for independent reading
16 editions published between 2001 and 2012 in English and held by 322 WorldCat member libraries worldwide
There are incredibly rich connections between classical analysis and number theory. For instance, analytic number theory contains many examples of asymptotic expressions derived from estimates for analytic functions, such as in the proof of the Prime Number Theorem. In combinatorial number theory, exact formulas for numbertheoretic quantities are derived from relations between analytic functions. Elliptic functions, especially theta functions, are an important class of such functions in this context, which had been made clear already in Jacobi's Fundamenta nova. Theta functions are also classically connected with Riemann surfaces and with the modular group $\Gamma = \mathrm{PSL}(2,\mathbb{Z})$, which provide another path for insights into number theory. Farkas and Kra, wellknown masters of the theory of Riemann surfaces and the analysis of theta functions, uncover here interesting combinatorial identities by means of the function theory on Riemann surfaces related to the principal congruence subgroups $\Gamma(k)$. For instance, the authors use this approach to derive congruences discovered by Ramanujan for the partition function, with the main ingredient being the construction of the same function in more than one way. The authors also obtain a variant on Jacobi's famous result on the number of ways that an integer can be represented as a sum of four squares, replacing the squares by triangular numbers and, in the process, obtaining a cleaner result. The recent trend of applying the ideas and methods of algebraic geometry to the study of theta functions and number theory has resulted in great advances in the area. However, the authors choose to stay with the classical point of view. As a result, their statements and proofs are very concrete. In this book the mathematician familiar with the algebraic geometry approach to theta functions and number theory will find many interesting ideas as well as detailed explanations and derivations of new and old results. Highlights of the book include systematic studies of theta constant identities, uniformizations of surfaces represented by subgroups of the modular group, partition identities, and Fourier coefficients of automorphic functions. Prerequisites are a solid understanding of complex analysis, some familiarity with Riemann surfaces, Fuchsian groups, and elliptic functions, and an interest in number theory. The book contains summaries of some of the required material, particularly for theta functions and theta constants. Readers will find here a careful exposition of a classical point of view of analysis and number theory. Presented are numerous examples plus suggestions for researchlevel problems. The text is suitable for a graduate course or for independent reading
In the tradition of Ahlfors and Bers : proceedings of the First AhlforsBers Colloquium, AhlforsBers Colloquium, November
68, 1998, State University of New York at Stony Brook by
AhlforsBers Colloquium(
Book
)
18 editions published between 2000 and 2012 in English and held by 263 WorldCat member libraries worldwide
18 editions published between 2000 and 2012 in English and held by 263 WorldCat member libraries worldwide
Quasiconformal mappings and Riemann surfaces by
S. L Krushkalʹ(
Book
)
10 editions published in 1979 in English and held by 261 WorldCat member libraries worldwide
10 editions published in 1979 in English and held by 261 WorldCat member libraries worldwide
Lipman Bers, a life in mathematics by
Linda Keen(
Book
)
9 editions published in 2015 in English and held by 129 WorldCat member libraries worldwide
The book is part biography and part collection of mathematical essays that gives the reader a perspective on the evolution of an interesting mathematical life. It is all about Lipman Bers, a giant in the mathematical world who lived in turbulent and exciting times. It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysisquasiconformal mappings and moduli of Riemann surfacesand the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global human rights and the end of political torture. The book contains autobiographical material and short reprints of his work. The main content is in the exposition of his research contributions, sometimes with novel points of view, by students, grandstudents, and colleagues. The research described was fundamental to the growth of a central part of 20th century mathematics that, now in the 21st century, is in a healthy state with much current interest and activity. The addition of personal recollections, professional tributes, and photographs yields a picture of a man, his personal and professional family, and his time
9 editions published in 2015 in English and held by 129 WorldCat member libraries worldwide
The book is part biography and part collection of mathematical essays that gives the reader a perspective on the evolution of an interesting mathematical life. It is all about Lipman Bers, a giant in the mathematical world who lived in turbulent and exciting times. It captures the essence of his mathematics, a development and transition from applied mathematics to complex analysisquasiconformal mappings and moduli of Riemann surfacesand the essence of his personality, a progression from a young revolutionary refugee to an elder statesman in the world of mathematics and a fighter for global human rights and the end of political torture. The book contains autobiographical material and short reprints of his work. The main content is in the exposition of his research contributions, sometimes with novel points of view, by students, grandstudents, and colleagues. The research described was fundamental to the growth of a central part of 20th century mathematics that, now in the 21st century, is in a healthy state with much current interest and activity. The addition of personal recollections, professional tributes, and photographs yields a picture of a man, his personal and professional family, and his time
Selected works of Lipman Bers : papers on complex analysis by
Lipman Bers(
Book
)
7 editions published in 1998 in English and held by 120 WorldCat member libraries worldwide
7 editions published in 1998 in English and held by 120 WorldCat member libraries worldwide
A Crash Course on Kleinian Groups : Lectures given at a special session at the January 1974 meeting of the American Mathematical
Society at San Francisco by
Lipman Bers(
)
2 editions published in 1974 in English and held by 98 WorldCat member libraries worldwide
2 editions published in 1974 in English and held by 98 WorldCat member libraries worldwide
Holomorphic functions and moduli : proceedings of a workshop held March 1319, 1986 by
D Drasin(
)
3 editions published in 1988 in English and held by 65 WorldCat member libraries worldwide
The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a miniconference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program
3 editions published in 1988 in English and held by 65 WorldCat member libraries worldwide
The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a miniconference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program
Holomorphic functions and moduli : proceedings of a workshop held March 1319, 1986 by
D Drasin(
)
2 editions published in 1988 in English and held by 56 WorldCat member libraries worldwide
The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a miniconference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program
2 editions published in 1988 in English and held by 56 WorldCat member libraries worldwide
The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a miniconference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program
Riemann surfaces by
Hershel M Farkas(
Book
)
11 editions published between 1979 and 1992 in English and Undetermined and held by 32 WorldCat member libraries worldwide
11 editions published between 1979 and 1992 in English and Undetermined and held by 32 WorldCat member libraries worldwide
Selected works of Lipman Bers : papers on complex analysis by
Lipman Bers(
Book
)
9 editions published in 1998 in English and held by 20 WorldCat member libraries worldwide
9 editions published in 1998 in English and held by 20 WorldCat member libraries worldwide
Riemann SurfaceseRelated Topics (AM97) Proceedings of the 1978 Stony Brook Conference by
Irwin Kra(
)
4 editions published between 1981 and 2016 in English and held by 16 WorldCat member libraries worldwide
The book description for the forthcoming "Riemann SurfaceseRelated Topics (AM97): Proceedings of the 1978 Stony Brook Conference. (AM97)" is not yet available
4 editions published between 1981 and 2016 in English and held by 16 WorldCat member libraries worldwide
The book description for the forthcoming "Riemann SurfaceseRelated Topics (AM97): Proceedings of the 1978 Stony Brook Conference. (AM97)" is not yet available
On the ring of holomorphic functions on an open Riemann surface by
Irwin Kra(
Book
)
4 editions published between 1966 and 1967 in English and held by 14 WorldCat member libraries worldwide
4 editions published between 1966 and 1967 in English and held by 14 WorldCat member libraries worldwide
A crash course on Kleinian groups by
Lipman Bers(
)
3 editions published between 1974 and 2008 in English and Undetermined and held by 13 WorldCat member libraries worldwide
3 editions published between 1974 and 2008 in English and Undetermined and held by 13 WorldCat member libraries worldwide
A Crash Course on Kleinian Groups, San Francisco, 1974 ; Lectures Given At a Special Session At the January 1974 Meeting of
the American Mathematical Society At San Francisco. Edited by Lipman Bers and Irwin Kra by
American Mathematical Society(
Book
)
2 editions published in 1974 in English and held by 10 WorldCat member libraries worldwide
2 editions published in 1974 in English and held by 10 WorldCat member libraries worldwide
more
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Audience Level
0 

1  
Kids  General  Special 
Related Identities
 Bers, Lipman Other Honoree Author Editor
 Farkas, Hershel M. Author
 Rodríguez, Rubí E. 1953 Other Author Editor
 Gilman, Jane 1945 Other Author
 Maskit, Bernard Other Contributor Editor
 Pogorelov, A. V. (Alekseĭ Vasilʹevich) 19192002 Author
 American Mathematical Society Other Publisher
 Zaustinskiy, Eugene
 Krushkalʹ, S. L. (Samuil Leĭbovich) Author
 Keen, Linda Author Editor
Useful Links
Associated Subjects
Automorphic functions Bers, Lipman Differential equations, Partial Functions Functions, Theta Functions of complex variables Geometry, Algebraic GeometryFoundations Global analysis (Mathematics) Group theory Holomorphic functions Kleinian groups Lie groups Mappings (Mathematics) Mathematical analysis Mathematicians Mathematics Modular groups Quasiconformal mappings Riemann surfaces Rings (Algebra) Teichmüller spaces Topological groups United States
Covers
Alternative Names
Irwin Kra American mathematician
Irwin Kra Amerikaans wiskundige
Irwin Kra amerikansk matematikar
Irwin Kra amerikansk matematiker
Irwin Kra matemàtic estatunidenc
Irwin Kra matemático estadounidense
Irwin Kra matematico statunitense
Irwin Kra matemáticu estauxunidense
Irwin Kra USamerikanischer Mathematiker
Kra, I.
Kra, I. 1937
Kra, Irvin
Kra, Irvin 1937
Kra, Irwin
Kra, Irwin 1937
Кра И.
Languages