Farkas, Hershel M.
Overview
Works:  13 works in 113 publications in 2 languages and 2,810 library holdings 

Genres:  Bibliography Conference papers and proceedings 
Roles:  Author, Editor 
Publication Timeline
.
Most widely held works by
Hershel M Farkas
Riemann surfaces by
Hershel M Farkas(
Book
)
29 editions published between 1979 and 2003 in English and Undetermined and held by 1,033 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 1,033 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
Generalizations of Thomae's formula for Zn curves by
Hershel M Farkas(
)
11 editions published between 2010 and 2011 in English and held by 455 WorldCat member libraries worldwide
Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces. "Generalizations of Thomae's Formula for Zn Curves" includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic
11 editions published between 2010 and 2011 in English and held by 455 WorldCat member libraries worldwide
Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces. "Generalizations of Thomae's Formula for Zn Curves" includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic
From fourier analysis and number theory to radon transforms and geometry : in memory of Leon Ehrenpreis by
Hershel M Farkas(
)
14 editions published between 2012 and 2014 in English and held by 408 WorldCat member libraries worldwide
This publication is an outgrowth of a memorial conference for Leon Ehrenpreis held at Temple University, November 1516, 2010. In the spirit of Ehrenpreis's contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis, and some applied mathematics. The papers in this volume generally contain all new results in the various fields in which Ehrenpreis worked. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore. A biographical sketch of Leon Ehrenpreis enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician and gentleman. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore. A biographical sketch of Leon Ehrenpreis enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician and gentleman
14 editions published between 2012 and 2014 in English and held by 408 WorldCat member libraries worldwide
This publication is an outgrowth of a memorial conference for Leon Ehrenpreis held at Temple University, November 1516, 2010. In the spirit of Ehrenpreis's contribution to mathematics, the papers in this volume, written by prominent mathematicians, represent the wide breadth of subjects that Ehrenpreis traversed in his career, including partial differential equations, combinatorics, number theory, complex analysis, and some applied mathematics. The papers in this volume generally contain all new results in the various fields in which Ehrenpreis worked. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore. A biographical sketch of Leon Ehrenpreis enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician and gentleman. The mature mathematician will find new mathematics and the advanced graduate student will find many new ideas to explore. A biographical sketch of Leon Ehrenpreis enhances the memorial tribute and gives the reader a glimpse into the life and career of a great mathematician and gentleman
Differential geometry and complex analysis : a volume dedicated to the memory of Harry Ernest Rauch by
Isaac Chavel(
Book
)
13 editions published between 1984 and 1985 in English and held by 334 WorldCat member libraries worldwide
This volume is dedicated to the memory of Harry Ernest Rauch, who died suddenly on June 18, 1979. In organizing the volume we solicited: (i) articles summarizing Rauch's own work in differential geometry, complex analysis and theta functions (ii) articles which would give the reader an idea of the depth and breadth of Rauch's researches, interests, and influence, in the fields he investigated, and (iii) articles of high scientific quality which would be of general interest. In each of the areas to which Rauch made significant contribution  pinching theorems, teichmiiller theory, and theta functions as they apply to Riemann surfaces  there has been substantial progress. Our hope is that the volume conveys the originality of Rauch's own work, the continuing vitality of the fields he influenced, and the enduring respect for, and tribute to, him and his accom plishments in the mathematical community. Finally, it is a pleasure to thank the Department of Mathematics, of the Grad uate School of the City University of New York, for their logistical support, James Rauch who helped us with the biography, and SpringerVerlag for all their efforts in producing this volume. Isaac Chavel . Hershel M. Farkas Contents Harry Ernest Rauch  Biographical Sketch. ... VII Bibliography of the Publications of H.E. Rauch. ... X Ph. D. Theses Written under the Supervision of H.E. Rauch. XIII H.E. Rauch, Geometre Differentiel (by M. Berger)
13 editions published between 1984 and 1985 in English and held by 334 WorldCat member libraries worldwide
This volume is dedicated to the memory of Harry Ernest Rauch, who died suddenly on June 18, 1979. In organizing the volume we solicited: (i) articles summarizing Rauch's own work in differential geometry, complex analysis and theta functions (ii) articles which would give the reader an idea of the depth and breadth of Rauch's researches, interests, and influence, in the fields he investigated, and (iii) articles of high scientific quality which would be of general interest. In each of the areas to which Rauch made significant contribution  pinching theorems, teichmiiller theory, and theta functions as they apply to Riemann surfaces  there has been substantial progress. Our hope is that the volume conveys the originality of Rauch's own work, the continuing vitality of the fields he influenced, and the enduring respect for, and tribute to, him and his accom plishments in the mathematical community. Finally, it is a pleasure to thank the Department of Mathematics, of the Grad uate School of the City University of New York, for their logistical support, James Rauch who helped us with the biography, and SpringerVerlag for all their efforts in producing this volume. Isaac Chavel . Hershel M. Farkas Contents Harry Ernest Rauch  Biographical Sketch. ... VII Bibliography of the Publications of H.E. Rauch. ... X Ph. D. Theses Written under the Supervision of H.E. Rauch. XIII H.E. Rauch, Geometre Differentiel (by M. Berger)
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
)
18 editions published between 2001 and 2012 in English and held by 317 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
18 editions published between 2001 and 2012 in English and held by 317 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
Theta functions with applications to Riemann surfaces by
Harry Ernest Rauch(
Book
)
10 editions published in 1974 in English and Italian and held by 223 WorldCat member libraries worldwide
10 editions published in 1974 in English and Italian and held by 223 WorldCat member libraries worldwide
Riemann surfaces by
Hershel M Farkas(
Book
)
11 editions published between 1979 and 1992 in English and Undetermined and held by 30 WorldCat member libraries worldwide
11 editions published between 1979 and 1992 in English and Undetermined and held by 30 WorldCat member libraries worldwide
Generalizations of Thomae's Formula for Zn Curves by
Hershel M Farkas(
)
2 editions published in 2011 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 2011 in English and held by 5 WorldCat member libraries worldwide
Alexander Zabrodsky in memoriam(
Book
)
1 edition published in 1989 in Undetermined and held by 2 WorldCat member libraries worldwide
1 edition published in 1989 in Undetermined and held by 2 WorldCat member libraries worldwide
Generalizations of Thomae's formula for Z sub n curves by
Hershel M Farkas(
Book
)
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
1 edition published in 2011 in English and held by 1 WorldCat member library worldwide
Generalizations of Thomae's Formula for Zn Curves by
Hershel M Farkas(
Book
)
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces. ""Generalizations of Thomae's Formula for Zn Curves"" includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic geometry
1 edition published in 2010 in English and held by 1 WorldCat member library worldwide
Previous publications on the generalization of the Thomae formulae to Zn curves have emphasized the theory's implications in mathematical physics and depended heavily on applied mathematical techniques. This book redevelops these previous results demonstrating how they can be derived directly from the basic properties of theta functions as functions on compact Riemann surfaces. ""Generalizations of Thomae's Formula for Zn Curves"" includes several refocused proofs developed in a generalized context that is more accessible to researchers in related mathematical fields such as algebraic geometry
Theta functions with applications to Riemann surfaces by
Harry E Rauch(
)
1 edition published in 1974 in English and held by 1 WorldCat member library worldwide
1 edition published in 1974 in English and held by 1 WorldCat member library worldwide
Generalizations of Thomae's Formula for Zn Curves(
)
1 edition published in 2011 in English and held by 0 WorldCat member libraries worldwide
1 edition published in 2011 in English and held by 0 WorldCat member libraries worldwide
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Related Identities
 Kra, Irwin
 Rauch, Harry Ernest 1925 Honoree Author Dedicatee
 Zemel, Shaul
 Ehrenpreis, Leon
 Chavel, Isaac Author Editor
 Knopp, Marvin I. Editor
 Gunning, Robert C. (Robert Clifford) 1931 Editor
 Taylor, B. A. 1939 Editor
 Zemel, Shaul
 Farjoun, Emmanuel Dror
Useful Links
Associated Subjects
Combinatorial analysis Curves, Algebraic Differential equations, Partial Fourier analysis Functions, Special Functions, Theta Functions of complex variables Geometry, Algebraic Geometry, Differential Global analysis (Mathematics) Global differential geometry Mathematics Modular groups Number theory Rauch, Harry Ernest, Riemann surfaces Topological groups
Covers
Alternative Names
Farkas, H. M.
Farkas, H. M. 1939
Farkas, Heršel M. 1939
Farkas, Hershel M.
Hershel Farkas American mathematician
Hershel Farkas Amerikaans wiskundige
Hershel Farkas israelischUSamerikanischer Mathematiker
Hershel Farkas matemàtic estatunidenc
Hershel Farkas matemático estadounidense
Languages