Spectral Methods of Automorphic Forms
Spectral Methods of Automorphic Forms

Author: Henryk Iwaniec

Publisher: American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain

Published: 2021-11-17

Total Pages: 220

ISBN-13: 1470466228

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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 book was an underground classic, both as a textbook and as a respected source for results, ideas, and references. Iwaniec treats the spectral theory of automorphic forms as the study of the space of $L^2$ functions on the upper half plane modulo a discrete subgroup. Key topics include Eisenstein series, estimates of Fourier coefficients, Kloosterman sums, the Selberg trace formula and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 Cole Prize for his fundamental contributions to number theory.

Spectral Decomposition and Eisenstein Series
Spectral Decomposition and Eisenstein Series

Author: Colette Moeglin

Publisher: Cambridge University Press

Published: 1995-11-02

Total Pages: 382

ISBN-13: 9780521418935

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A self-contained introduction to automorphic forms, and Eisenstein series and pseudo-series, proving some of Langlands' work at the intersection of number theory and group theory.

Topics in Classical Automorphic Forms
Topics in Classical Automorphic Forms

Author: Henryk Iwaniec

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 274

ISBN-13: 0821807773

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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

Six Short Chapters on Automorphic Forms and L-functions
Six Short Chapters on Automorphic Forms and L-functions

Author: Ze-Li Dou

Publisher: Springer Science & Business Media

Published: 2012-12-15

Total Pages: 131

ISBN-13: 3642287085

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"Six Short Chapters on Automorphic Forms and L-functions" treats the period conjectures of Shimura and the moment conjecture. These conjectures are of central importance in contemporary number theory, but have hitherto remained little discussed in expository form. The book is divided into six short and relatively independent chapters, each with its own theme, and presents a motivated and lively account of the main topics, providing professionals an overall view of the conjectures and providing researchers intending to specialize in the area a guide to the relevant literature. Ze-Li Dou and Qiao Zhang are both associate professors of Mathematics at Texas Christian University, USA.

L-Functions and Automorphic Forms
L-Functions and Automorphic Forms

Author: Jan Hendrik Bruinier

Publisher: Springer

Published: 2018-02-22

Total Pages: 367

ISBN-13: 3319697129

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This book presents a collection of carefully refereed research articles and lecture notes stemming from the Conference "Automorphic Forms and L-Functions", held at the University of Heidelberg in 2016. The theory of automorphic forms and their associated L-functions is one of the central research areas in modern number theory, linking number theory, arithmetic geometry, representation theory, and complex analysis in many profound ways. The 19 papers cover a wide range of topics within the scope of the conference, including automorphic L-functions and their special values, p-adic modular forms, Eisenstein series, Borcherds products, automorphic periods, and many more.

Automorphic Forms and Related Topics
Automorphic Forms and Related Topics

Author: Samuele Anni

Publisher: American Mathematical Soc.

Published: 2019-06-19

Total Pages: 298

ISBN-13: 147043525X

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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.

Modern Analysis of Automorphic Forms By Example
Modern Analysis of Automorphic Forms By Example

Author: Paul Garrett

Publisher: Cambridge University Press

Published: 2018-09-20

Total Pages: 407

ISBN-13: 1107154006

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Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Modern Analysis of Automorphic Forms By Example: Volume 1
Modern Analysis of Automorphic Forms By Example: Volume 1

Author: Paul Garrett

Publisher: Cambridge University Press

Published: 2018-09-20

Total Pages: 407

ISBN-13: 1108228240

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This is Volume 1 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 1 features critical results, which are proven carefully and in detail, including discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. Volume 2 features automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.

Modern Analysis of Automorphic Forms By Example: Volume 2
Modern Analysis of Automorphic Forms By Example: Volume 2

Author: Paul Garrett

Publisher: Cambridge University Press

Published: 2018-09-20

Total Pages: 367

ISBN-13: 1108669212

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This is Volume 2 of a two-volume book that provides a self-contained introduction to the theory and application of automorphic forms, using examples to illustrate several critical analytical concepts surrounding and supporting the theory of automorphic forms. The two-volume book treats three instances, starting with some small unimodular examples, followed by adelic GL2, and finally GLn. Volume 2 features critical results, which are proven carefully and in detail, including automorphic Green's functions, metrics and topologies on natural function spaces, unbounded operators, vector-valued integrals, vector-valued holomorphic functions, and asymptotics. Volume 1 features discrete decomposition of cuspforms, meromorphic continuation of Eisenstein series, spectral decomposition of pseudo-Eisenstein series, and automorphic Plancherel theorem. With numerous proofs and extensive examples, this classroom-tested introductory text is meant for a second-year or advanced graduate course in automorphic forms, and also as a resource for researchers working in automorphic forms, analytic number theory, and related fields.