Panchishkin, A. A. (Alekseĭ Alekseevich)
Overview
Works:  46 works in 128 publications in 2 languages and 2,146 library holdings 

Roles:  Author, Thesis advisor 
Publication Timeline
.
Most widely held works by
A. A Panchishkin
Introduction to modern number theory : fundamental problems, ideas and theories by
Yuri Ivanovic Manin(
)
24 editions published between 2005 and 2007 in English and held by 900 WorldCat member libraries worldwide
"Introduction to Modern Number Theory surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include nonAbelian generalizations of class field theory, recursive computability and Diophantine equations, zeta and Lfunctions."Jacket
24 editions published between 2005 and 2007 in English and held by 900 WorldCat member libraries worldwide
"Introduction to Modern Number Theory surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include nonAbelian generalizations of class field theory, recursive computability and Diophantine equations, zeta and Lfunctions."Jacket
NonArchimedean Lfunctions of Siegel and Hilbert modular forms by
Aleksej A Pančiškin(
Book
)
17 editions published between 1900 and 2013 in English and Undetermined and held by 423 WorldCat member libraries worldwide
This book is devoted to the arithmetical theory of Siegel modular forms and their Lfunctions. The central object are Lfunctions of classical Siegel modular forms whose special values are studied using the RankinSelberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of padic interpolation of these critical values is presented. An important class of padic Lfunctions treated in the present book are padic Lfunctions of Siegel modular forms having logarithmic growth (which were first introduced by Amice, Velu and Vishik in the elliptic modular case when they come from a good supersingular reduction of ellptic curves and abelian varieties). The given construction of these padic Lfunctions uses precise algebraic properties of the arihmetical Shimura differential operator. The book could be very useful for postgraduate students and for nonexperts giving a quick access to a rapidly developping domain of algebraic number theory: the arithmetical theory of Lfunctions and modular forms
17 editions published between 1900 and 2013 in English and Undetermined and held by 423 WorldCat member libraries worldwide
This book is devoted to the arithmetical theory of Siegel modular forms and their Lfunctions. The central object are Lfunctions of classical Siegel modular forms whose special values are studied using the RankinSelberg method and the action of certain differential operators on modular forms which have nice arithmetical properties. A new method of padic interpolation of these critical values is presented. An important class of padic Lfunctions treated in the present book are padic Lfunctions of Siegel modular forms having logarithmic growth (which were first introduced by Amice, Velu and Vishik in the elliptic modular case when they come from a good supersingular reduction of ellptic curves and abelian varieties). The given construction of these padic Lfunctions uses precise algebraic properties of the arihmetical Shimura differential operator. The book could be very useful for postgraduate students and for nonexperts giving a quick access to a rapidly developping domain of algebraic number theory: the arithmetical theory of Lfunctions and modular forms
NonArchimedean Lfunctions and arithmetical Siegel modular forms by
Michel Courtieu(
Book
)
17 editions published between 2003 and 2004 in English and held by 386 WorldCat member libraries worldwide
17 editions published between 2003 and 2004 in English and held by 386 WorldCat member libraries worldwide
Number theory I : fundamental problems, ideas and theories by
I︠U︡. I Manin(
Book
)
6 editions published between 1992 and 2005 in English and held by 269 WorldCat member libraries worldwide
6 editions published between 1992 and 2005 in English and held by 269 WorldCat member libraries worldwide
Introduction to modern number theory : fundamental problems, ideas and theories by
Yuri Ivanovic Manin(
Book
)
1 edition published in 2005 in English and held by 19 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 19 WorldCat member libraries worldwide
Introduction to modern number theory : fundamental problems, ideas and theories by
Jurij I Manin(
Book
)
1 edition published in 2007 in English and held by 17 WorldCat member libraries worldwide
1 edition published in 2007 in English and held by 17 WorldCat member libraries worldwide
Introduction to Modern Number Theory : Fundamental Problems, Ideas and Theories by
Yuri Ivanovic Manin(
)
2 editions published in 2005 in English and held by 13 WorldCat member libraries worldwide
2 editions published in 2005 in English and held by 13 WorldCat member libraries worldwide
NonArchimedean Lfunctions of Siegel and Hilbert modular forms by
Michel Courtieu(
)
3 editions published between 1991 and 2004 in English and held by 11 WorldCat member libraries worldwide
3 editions published between 1991 and 2004 in English and held by 11 WorldCat member libraries worldwide
Introduction to Modern Number Theory : Fundamental Problems, Ideas and Theories by
Yuri Ivanovic Manin(
)
2 editions published in 2005 in English and held by 8 WorldCat member libraries worldwide
2 editions published in 2005 in English and held by 8 WorldCat member libraries worldwide
NonArchimedean Lfunction of Siegel and Hilbert modular forms by
Alexey A Panchishkin(
Book
)
1 edition published in 1991 in English and held by 8 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 8 WorldCat member libraries worldwide
NonArchimedean Lfunctions and arithmetical of Siegel and Hilbert modular forms by
Michel Courtieu(
Book
)
2 editions published in 2004 in English and held by 6 WorldCat member libraries worldwide
2 editions published in 2004 in English and held by 6 WorldCat member libraries worldwide
Nonarchimedean Lfunctions of Siegel and Hilbert modilar forms by
Alexey A Panchishkin(
Book
)
1 edition published in 1991 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1991 in English and held by 6 WorldCat member libraries worldwide
Introduction to modern number theory : fundamental problems, ideas and theories(
)
1 edition published in 2005 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 6 WorldCat member libraries worldwide
Trigonometric functions (Problemsolving approach) by
A Panchishkin(
Book
)
6 editions published in 1988 in English and Undetermined and held by 6 WorldCat member libraries worldwide
6 editions published in 1988 in English and Undetermined and held by 6 WorldCat member libraries worldwide
Trigonometricheskie funkt︠s︡ii v zadachakh by
A. A Panchishkin(
Book
)
2 editions published in 1986 in Russian and held by 6 WorldCat member libraries worldwide
2 editions published in 1986 in Russian and held by 6 WorldCat member libraries worldwide
Trigonometričeskie funkcii v zadačach by
Aleksej Alekseevič Pančiškin(
Book
)
4 editions published in 1986 in Russian and held by 5 WorldCat member libraries worldwide
4 editions published in 1986 in Russian and held by 5 WorldCat member libraries worldwide
Introduction to Modern Number Theory : Fundamental Problems, Ideas and Theories by
Yuri Ivanovic Manin(
)
1 edition published in 2005 in English and held by 5 WorldCat member libraries worldwide
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include nonAbelian generalizations of class field theory, recursive computability and Diophantine equations, zeta and Lfunctions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects. From the reviews of the 2nd edition: "... For my part, I come to praise this fine volume. This book is a highly instructive read ... the quality, knowledge, and expertise of the authors shines through. ... The present volume is almost startlingly uptodate ..." (A. van der Poorten, Gazette, Australian Math. Soc. 34 (1), 2007)
1 edition published in 2005 in English and held by 5 WorldCat member libraries worldwide
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include nonAbelian generalizations of class field theory, recursive computability and Diophantine equations, zeta and Lfunctions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects. From the reviews of the 2nd edition: "... For my part, I come to praise this fine volume. This book is a highly instructive read ... the quality, knowledge, and expertise of the authors shines through. ... The present volume is almost startlingly uptodate ..." (A. van der Poorten, Gazette, Australian Math. Soc. 34 (1), 2007)
Motives for absolute Hodge cycles by
A. A Panchishkin(
Book
)
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1992 in English and held by 5 WorldCat member libraries worldwide
Introduction to modern number theory : fundamental problems, ideas and theories by I⁻ŁU. I Manin(
)
1 edition published in 2005 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 4 WorldCat member libraries worldwide
Introduction to Modern Number Theory(
)
1 edition published in 2005 in English and held by 4 WorldCat member libraries worldwide
1 edition published in 2005 in English and held by 4 WorldCat member libraries worldwide
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Audience Level
0 

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Kids  General  Special 
Related Identities
 Manin, I︠U︡. I. Author
 Courtieu, Michel 1973 Author Creator
 Паршин, А. Н Editor
 Шафаревич, И. Р (Игорь Ростиславович) 1923 Editor
 Shavgulidze, E.
 Shavgulidze, E. T. (Evgeniĭ Tengizovich)
 SpringerVerlag Publisher
 Manin, Yuri Ivanovic Author
 MaxPlanckInstitut für Mathematik (Bonn)
 Manin, I⁻ŁU. I. Author
Associated Subjects
Algebraic number theory Automorphic forms Data encryption (Computer science) Diophantine analysis Discontinuous groups Forms, Modular Functions, Zeta Geometry, Algebraic Hilbert modular surfaces Lfunctions Logic, Symbolic and mathematical Mathematical physics Mathematics Modular groups Nonstandard mathematical analysis Number theory Physics Siegel domains Trigonometrical functions Trigonometry
Covers
Alternative Names
Panchishkin, A. 1953
Panchishkin, A. A.
Panchishkin, A. A. 1953
Panchishkin, A. A. (Aleksei Alekseevich), 1953
Panchishkin, Alekseĭ Alekseevich
Panchishkin, Aleksei Alekseevich 1953
Panchishkin, Alexei.
Panchishkin, Alexei 1953
Panchishkin, Alexei A.
Panchishkin, Alexei A. 1953
Panchishkin, Alexej A. 1953
Panchishkin, Alexey.
Panchishkin, Alexey A.
Panchishkin, Alexey A. 1953
Panchishkin Alexey Alekseevich
Panchishkin, Alexey Alekseevich, 1953
Pančiškin, A. 1953
Pančiškin, A. A.
Pančiškin, A. A. 1953
Pančiškin, Aleksej A.
Pančiškin, Aleksej Alekseevič 1953
Pantchichkine, Alexei, 1953
Панчишкин Алексей Алексеевич
Languages