Topics In Classical Automorphic Forms

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Topics In Classical Automorphic Forms

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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 1997

Topics In Classical Automorphic Forms written by Henryk Iwaniec 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 1997 with Mathematics categories.

This volume discusses various perspectives of the theory of automorphic forms drawn from the author's notes from a Rutgers University graduate course. In addition to detailed and often nonstandard treatment of familiar theoretical topics, the author also gives special attention to such subjects as theta- functions and representatives by quadratic forms. Annotation copyrighted by Book News, Inc., Portland, OR

Spectral Methods Of Automorphic Forms

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Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Spectral Methods Of Automorphic Forms written by Henryk Iwaniec 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 2002 with Mathematics categories.

Automorphic forms are one of the central topics of analytic number theory. In fact, they sit at the confluence of analysis, algebra, geometry, and number theory. In this book, Henryk Iwaniec once again displays his penetrating insight, powerful analytic techniques, and lucid writing style. The first edition of this volume was an underground classic, both as a textbook and as a respected source for results, ideas, and references. The book's reputation sparked a growing interest inthe mathematical community to bring it back into print. The AMS has answered that call with the publication of this second edition. In the book, Iwaniec treats the spectral theory of automorphic forms as the study of the space $L2 (H\Gamma)$, where $H$ is the upper half-plane and $\Gamma$ is a discretesubgroup of volume-preserving transformations of $H$. He combines various techniques from analytic number theory. Among the topics discussed are Eisenstein series, estimates for Fourier coefficients of automorphic forms, the theory of Kloosterman sums, the Selberg trace formula, and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 AMS Cole Prize for his fundamental contributions to analytic number theory. Also available from the AMS by H. Iwaniec is Topics in ClassicalAutomorphic Forms, Volume 17 in the Graduate Studies in Mathematics series. The book is designed for graduate students and researchers working in analytic number theory.

Siegel Modular Forms

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Author : Ameya Pitale
language : en
Publisher: Springer
Release Date : 2019-05-07

Siegel Modular Forms written by Ameya Pitale and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-07 with Mathematics categories.

This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the areaas a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.

Modular Forms And Related Topics In Number Theory

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Author : B. Ramakrishnan
language : en
Publisher: Springer Nature
Release Date : 2020-11-24

Modular Forms And Related Topics In Number Theory written by B. Ramakrishnan and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-24 with Mathematics categories.

This book collects the papers presented at the Conference on Number Theory, held at the Kerala School of Mathematics, Kozhikode, Kerala, India, from December 10–14, 2018. The conference aimed at bringing the active number theorists and researchers in automorphic forms and allied areas to demonstrate their current research works. This book benefits young research scholars, postdoctoral fellows, and young faculty members working in these areas of research.

Eisenstein Series And Automorphic Representations

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Author : Philipp Fleig
language : en
Publisher: Cambridge Studies in Advanced
Release Date : 2018-07-05

Eisenstein Series And Automorphic Representations written by Philipp Fleig and has been published by Cambridge Studies in Advanced this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-05 with Mathematics categories.

Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Automorphic Forms And Related Topics

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Author : Samuele Anni
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-19

Automorphic Forms And Related Topics written by Samuele Anni 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 2019-06-19 with Mathematics categories.

This volume contains the proceedings of the Building Bridges: 3rd EU/US Summer School and Workshop on Automorphic Forms and Related Topics, which was held in Sarajevo from July 11–22, 2016. The articles summarize material which was presented during the lectures and speed talks during the workshop. These articles address various aspects of the theory of automorphic forms and its relations with the theory of L-functions, the theory of elliptic curves, and representation theory. In addition to mathematical content, the workshop held a panel discussion on diversity and inclusion, which was chaired by a social scientist who has contributed to this volume as well. This volume is intended for researchers interested in expanding their own areas of focus, thus allowing them to “build bridges” to mathematical questions in other fields.

Modular Forms Basics And Beyond

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Author : Goro Shimura
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-18

Modular Forms Basics And Beyond written by Goro Shimura 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 2011-11-18 with Mathematics categories.

This is an advanced book on modular forms. While there are many books published about modular forms, they are written at an elementary level, and not so interesting from the viewpoint of a reader who already knows the basics. This book offers something new, which may satisfy the desire of such a reader. However, we state every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically.

The Descent Map From Automorphic Representations Of Gl N To Classical Groups

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Author : David Soudry
language : en
Publisher: World Scientific
Release Date : 2011-06-30

The Descent Map From Automorphic Representations Of Gl N To Classical Groups written by David Soudry and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-30 with Mathematics categories.

This book introduces the method of automorphic descent, providing an explicit inverse map to the (weak) Langlands functorial lift from generic, cuspidal representations on classical groups to general linear groups. The essence of this method is the study of certain Fourier coefficients of Gelfand-Graev type, or of Fourier-Jacobi type when applied to certain residual Eisenstein series. This book contains a complete account of this automorphic descent, with complete, detailed proofs. The book will be of interest to graduate students and mathematicians, who specialize in automorphic forms and in representation theory of reductive groups over local fields. Relatively self-contained, the content of some of the chapters can serve as topics for graduate students seminars.

Automorphic Forms

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Author : Anton Deitmar
language : en
Publisher: Springer
Release Date : 2012-08-29

Automorphic Forms written by Anton Deitmar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.

Automorphic forms are an important complex analytic tool in number theory and modern arithmetic geometry. They played for example a vital role in Andrew Wiles's proof of Fermat's Last Theorem. This text provides a concise introduction to the world of automorphic forms using two approaches: the classic elementary theory and the modern point of view of adeles and representation theory. The reader will learn the important aims and results of the theory by focussing on its essential aspects and restricting it to the 'base field' of rational numbers. Students interested for example in arithmetic geometry or number theory will find that this book provides an optimal and easily accessible introduction into this topic.

Conformal Field Theory Automorphic Forms And Related Topics

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Author : Winfried Kohnen
language : en
Publisher: Springer
Release Date : 2014-08-22

Conformal Field Theory Automorphic Forms And Related Topics written by Winfried Kohnen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-22 with Mathematics categories.

This book, part of the series Contributions in Mathematical and Computational Sciences, reviews recent developments in the theory of vertex operator algebras (VOAs) and their applications to mathematics and physics. The mathematical theory of VOAs originated from the famous monstrous moonshine conjectures of J.H. Conway and S.P. Norton, which predicted a deep relationship between the characters of the largest simple finite sporadic group, the Monster and the theory of modular forms inspired by the observations of J. MacKay and J. Thompson. The contributions are based on lectures delivered at the 2011 conference on Conformal Field Theory, Automorphic Forms and Related Topics, organized by the editors as part of a special program offered at Heidelberg University that summer under the sponsorship of the Mathematics Center Heidelberg (MATCH).