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Automorphic Forms And Zeta Functions

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Automorphic Forms And Zeta Functions Proceedings Of The Conference In Memory Of Tsuneo Arakawa

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Author : Masanobu Kaneko
language : en
Publisher: World Scientific
Release Date : 2006-01-03

Automorphic Forms And Zeta Functions Proceedings Of The Conference In Memory Of Tsuneo Arakawa written by Masanobu Kaneko and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-03 with Mathematics categories.

Automorphic Forms And Zeta Functions

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Author : Siegfried Bcherer
language : en
Publisher: World Scientific
Release Date : 2006

Automorphic Forms And Zeta Functions written by Siegfried Bcherer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.

This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L -functions, many of which are closely related to Arakawa''s works. This collection of papers illustrates Arakawa''s contributions and the current trends in modular forms in several variables and related zeta functions. Contents: Tsuneo Arakawa and His Works; Estimate of the Dimensions of Hilbert Modular Forms by Means of Differential Operators (H Aoki); MarsdenOCoWeinstein Reduction, Orbits and Representations of the Jacobi Group (R Berndt); On Eisenstein Series of Degree Two for Squarefree Levels and the Genus Version of the Basis Problem I (S BAcherer); Double Zeta Values and Modular Forms (H Gangl et al.); Type Numbers and Linear Relations of Theta Series for Some General Orders of Quaternion Algebras (K-I Hashimoto); Skew-Holomorphic Jacobi Forms of Higher Degree (S Hayashida); A Hermitian Analog of the Schottky Form (M Hentschel & A Krieg); The Siegel Series and Spherical Functions on O (2 n) / (O (n) x O (n) ) (Y Hironaka & F Sato); KoecherOCoMaa Series for Real Analytic Siegel Eisenstein Series (T Ibukiyama & H Katsurada); A Short History on Investigation of the Special Values of Zeta and L -Functions of Totally Real Number Fields (T Ishii & T Oda); Genus Theta Series, Hecke Operators and the Basis Problem for Eisenstein Series (H Katsurada & R Schulze-Pillot); The Quadratic Mean of Automorphic L -Functions (W Kohnen et al.); Inner Product Formula for Kudla Lift (A Murase & T Sugano); On Certain Automorphic Forms of Sp (1, q ) (Arakawa''s Results and Recent Progress) (H-A Narita); On Modular Forms for the Paramodular Groups (B Roberts & R Schmidt); SL(2, Z)-Invariant Spaces Spanned by Modular Units (N-P Skoruppa & W Eholzer). Readership: Researchers and graduate students in number theory or representation theory as well as in mathematical physics or combinatorics."

Automorphic Forms And Zeta Functions

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Author : Siegfried Bcherer
language : en
Publisher: World Scientific
Release Date : 2006

This volume contains a valuable collection of articles presented at a conference on Automorphic Forms and Zeta Functions in memory of Tsuneo Arakawa, an eminent researcher in modular forms in several variables and zeta functions. The book begins with a review of his works, followed by 16 articles by experts in the fields including H Aoki, R Berndt, K Hashimoto, S Hayashida, Y Hironaka, H Katsurada, W Kohnen, A Krieg, A Murase, H Narita, T Oda, B Roberts, R Schmidt, R Schulze-Pillot, N Skoruppa, T Sugano, and D Zagier. A variety of topics in the theory of modular forms and zeta functions are covered: Theta series and the basis problems, Jacobi forms, automorphic forms on Sp(1, q), double zeta functions, special values of zeta and L-functions, many of which are closely related to Arakawa's works. This collection of papers illustrates Arakawa's contributions and the current trends in modular forms in several variables and related zeta functions. Contents: Tsuneo Arakawa and His Works; Estimate of the Dimensions of Hilbert Modular Forms by Means of Differential Operator (H Aoki); Marsden-Weinstein Reduction, Orbits and Representations of the Jacobi Group (R Berndt); On Eisenstein Series of Degree Two for Squarefree Levels and the Genus Version of the Basis Problem I (S Bocherer); Double Zeta Values and Modular Forms (H Gangl et al.); Type Numbers and Linear Relations of Theta Series for Some General Orders of Quaternion Algebras (K Hashimoto); Skewholomorphic Jacobi Forms of Higher Degree (S Hayashida); A Hermitian Analog of the Schottky Form (M Hentschel & A Krieg); The Siegel Series and Spherical Functions on O(2n)/(O(n) x O(n)) (Y Hironaka & F Sati); Koecher-Maa Series for Real Analytic Siegel Eisenstein Series (T Ibukiyama & H Katsurada); A Short History on Investigation of the Special Values of Zeta and L-Functions of Totally Real Number Fields (T Ishii & T Oda); Genus Theta Series, Hecke Operators and the Basis Problem for Eisenstein Series (H Katsurada & R Schulze-Pillot); The Quadratic Mean of Automorphic L-Functions (W Kohnen et al.); Inner Product Formula for Kudla Lift (A Murase & T Sugano); On Certain Automorphic Forms of Sp(1,q) (Arakawa's Results and Recent Progress) (H Narita); On Modular Forms for the Paramodular Group (B Roberts & R Schmidt); SL(2,Z)-Invariant Spaces Spanned by Modular Units (N-P Skoruppa & W Eholzer). Readership: Researchers and graduate students in number theory or representation theory as well as in mathematical physics or combinatorics.

Introduction To The Arithmetic Theory Of Automorphic Functions

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Author : Gorō Shimura
language : en
Publisher: Princeton University Press
Release Date : 1971-08-21

Introduction To The Arithmetic Theory Of Automorphic Functions written by Gorō Shimura and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-08-21 with Mathematics categories.

The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.

Zeta Functions Of Simple Algebras

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Author : Roger Godement
language : en
Publisher: Springer
Release Date : 2006-11-14

Zeta Functions Of Simple Algebras written by Roger Godement and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Arithmeticity In The Theory Of Automorphic Forms

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Author : Goro Shimura
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Arithmeticity In The Theory Of Automorphic Forms written by Goro Shimura and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

Written by one of the leading experts, venerable grandmasters, and most active contributors $\ldots$ in the arithmetic theory of automorphic forms $\ldots$ the new material included here is mainly the outcome of his extensive work $\ldots$ over the last eight years $\ldots$ a very careful, detailed introduction to the subject $\ldots$ this monograph is an important, comprehensively written and profound treatise on some recent achievements in the theory. --Zentralblatt MATH The main objects of study in this book are Eisenstein series and zeta functions associated with Hecke eigenforms on symplectic and unitary groups. After preliminaries--including a section, ``Notation and Terminology''--the first part of the book deals with automorphic forms on such groups. In particular, their rationality over a number field is defined and discussed in connection with the group action; also the reciprocity law for the values of automorphic functions at CM-points is proved. Next, certain differential operators that raise the weight are investigated in higher dimension. The notion of nearly holomorphic functions is introduced, and their arithmeticity is defined. As applications of these, the arithmeticity of the critical values of zeta functions and Eisenstein series is proved. Though the arithmeticity is given as the ultimate main result, the book discusses many basic problems that arise in number-theoretical investigations of automorphic forms but that cannot be found in expository forms. Examples of this include the space of automorphic forms spanned by cusp forms and certain Eisenstein series, transformation formulas of theta series, estimate of the Fourier coefficients of modular forms, and modular forms of half-integral weight. All these are treated in higher-dimensional cases. The volume concludes with an Appendix and an Index. The book will be of interest to graduate students and researchers in the field of zeta functions and modular forms.

Introduction To Siegel Modular Forms And Dirichlet Series

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Author : Anatoli Andrianov
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-22

Introduction To Siegel Modular Forms And Dirichlet Series written by Anatoli Andrianov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-22 with Mathematics categories.

Several years ago I was invited to an American university to give one-term graduate course on Siegel modular forms, Hecke operators, and related zeta functions. The idea to present in a concise but basically complete and self-contained form an int- duction to an important and developing area based partly on my own work attracted me. I accepted the invitation and started to prepare the course. Unfortunately, the visit was not realized. But the idea of such a course continued to be alive till after a number of years this book was ?nally completed. I hope that this short book will serve to attract young researchers to this beautiful ?eld, and that it will simplify and make more pleasant the initial steps. No special knowledge is presupposed for reading this book beyond standard courses in algebra and calculus (one and several variables), although some skill in working with mathematical texts would be helpful. The reader will judge whether the result was worth the effort. Dedications. The ideas of Goro Shimura exerted a deep in?uence on the number theory of the second half of the twentieth century in general and on the author’s formation in particular. When Andre ` Weil was signing a copy of his “Basic Number Theory” to my son, he wrote in Russian, ”To Fedor Anatolievich hoping that he will become a number theoretist”. Fedor has chosen computer science. Now I pass on the idea to Fedor’s daughter, Alexandra Fedorovna.

Automorphic Forms And Geometry Of Arithmetic Varieties

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Author : K. Hashimoto
language : en
Publisher: Academic Press
Release Date : 2014-07-14

Automorphic Forms And Geometry Of Arithmetic Varieties written by K. Hashimoto and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.

Automorphic Forms and Geometry of Arithmetic Varieties deals with the dimension formulas of various automorphic forms and the geometry of arithmetic varieties. The relation between two fundamental methods of obtaining dimension formulas (for cusp forms), the Selberg trace formula and the index theorem (Riemann-Roch's theorem and the Lefschetz fixed point formula), is examined. Comprised of 18 sections, this volume begins by discussing zeta functions associated with cones and their special values, followed by an analysis of cusps on Hilbert modular varieties and values of L-functions. The reader is then introduced to the dimension formula of Siegel modular forms; the graded rings of modular forms in several variables; and Selberg-Ihara's zeta function for p-adic discrete groups. Subsequent chapters focus on zeta functions of finite graphs and representations of p-adic groups; invariants and Hodge cycles; T-complexes and Ogata's zeta zero values; and the structure of the icosahedral modular group. This book will be a useful resource for mathematicians and students of mathematics.

Introduction To The Arithmetic Theory Of Automorphic Functions

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Author : Gorō Shimura
language : en
Publisher: Princeton University Press
Release Date : 1971-08-21

Automorphic Forms On Gl 2

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Author : H. Jacquet
language : en
Publisher: Springer
Release Date : 2006-11-15

Automorphic Forms On Gl 2 written by H. Jacquet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Automorphic Forms And Zeta Functions

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