Contributions To Automorphic Forms Geometry And Number Theory

Author : Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi
Publisher : JHU Press
Page : 946 pages
File Size : 48,5 Mb
Release : 2004-03-11
Category : Mathematics
ISBN : 0801878608

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Contributions to Automorphic Forms, Geometry, and Number Theory by Haruzo Hida,Dinakar Ramakrishnan,Freydoon Shahidi Pdf

In Contributions to Automorphic Forms, Geometry, and Number Theory, Haruzo Hida, Dinakar Ramakrishnan, and Freydoon Shahidi bring together a distinguished group of experts to explore automorphic forms, principally via the associated L-functions, representation theory, and geometry. Because these themes are at the cutting edge of a central area of modern mathematics, and are related to the philosophical base of Wiles' proof of Fermat's last theorem, this book will be of interest to working mathematicians and students alike. Never previously published, the contributions to this volume expose the reader to a host of difficult and thought-provoking problems. Each of the extraordinary and noteworthy mathematicians in this volume makes a unique contribution to a field that is currently seeing explosive growth. New and powerful results are being proved, radically and continually changing the field's make up. Contributions to Automorphic Forms, Geometry, and Number Theory will likely lead to vital interaction among researchers and also help prepare students and other young mathematicians to enter this exciting area of pure mathematics. Contributors: Jeffrey Adams, Jeffrey D. Adler, James Arthur, Don Blasius, Siegfried Boecherer, Daniel Bump, William Casselmann, Laurent Clozel, James Cogdell, Laurence Corwin, Solomon Friedberg, Masaaki Furusawa, Benedict Gross, Thomas Hales, Joseph Harris, Michael Harris, Jeffrey Hoffstein, Hervé Jacquet, Dihua Jiang, Nicholas Katz, Henry Kim, Victor Kreiman, Stephen Kudla, Philip Kutzko, V. Lakshmibai, Robert Langlands, Erez Lapid, Ilya Piatetski-Shapiro, Dipendra Prasad, Stephen Rallis, Dinakar Ramakrishnan, Paul Sally, Freydoon Shahidi, Peter Sarnak, Rainer Schulze-Pillot, Joseph Shalika, David Soudry, Ramin Takloo-Bigash, Yuri Tschinkel, Emmanuel Ullmo, Marie-France Vignéras, Jean-Loup Waldspurger.

Author : Haruzo Hida
Publisher : Unknown
Page : 910 pages
File Size : 48,6 Mb
Release : 2004
Category : Electronic
ISBN : OCLC:1072733852

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Contributions to automorphic forms, geometry, and number theory by Haruzo Hida Pdf

Author : Bruce C. Berndt,Ken Ono
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 50,9 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781475760446

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Number Theory and Modular Forms by Bruce C. Berndt,Ken Ono Pdf

Robert A. Rankin, one of the world's foremost authorities on modular forms and a founding editor of The Ramanujan Journal, died on January 27, 2001, at the age of 85. Rankin had broad interests and contributed fundamental papers in a wide variety of areas within number theory, geometry, analysis, and algebra. To commemorate Rankin's life and work, the editors have collected together 25 papers by several eminent mathematicians reflecting Rankin's extensive range of interests within number theory. Many of these papers reflect Rankin's primary focus in modular forms. It is the editors' fervent hope that mathematicians will be stimulated by these papers and gain a greater appreciation for Rankin's contributions to mathematics. This volume would be an inspiration to students and researchers in the areas of number theory and modular forms.

Author : Jan Hendrik Bruinier,Winfried Kohnen
Publisher : Springer
Page : 366 pages
File Size : 46,9 Mb
Release : 2018-02-22
Category : Mathematics
ISBN : 9783319697123

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L-Functions and Automorphic Forms by Jan Hendrik Bruinier,Winfried Kohnen Pdf

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.

Author : Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang
Publisher : Birkhäuser
Page : 214 pages
File Size : 53,9 Mb
Release : 2008-11-01
Category : Mathematics
ISBN : 0817671293

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Representation Theory and Automorphic Forms by Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang Pdf

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.

Author : Valentin Blomer,Preda Mihăilescu
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 40,7 Mb
Release : 2011-11-19
Category : Mathematics
ISBN : 9781461412199

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Contributions in Analytic and Algebraic Number Theory by Valentin Blomer,Preda Mihăilescu Pdf

The text that comprises this volume is a collection of surveys and original works from experts in the fields of algebraic number theory, analytic number theory, harmonic analysis, and hyperbolic geometry. A portion of the collected contributions have been developed from lectures given at the "International Conference on the Occasion of the 60th Birthday of S. J. Patterson", held at the University Göttingen, July 27-29 2009. Many of the included chapters have been contributed by invited participants. This volume presents and investigates the most recent developments in various key topics in analytic number theory and several related areas of mathematics. The volume is intended for graduate students and researchers of number theory as well as applied mathematicians interested in this broad field.

Author : K. Hashimoto,Y. Namikawa
Publisher : Academic Press
Page : 540 pages
File Size : 42,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781483218076

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Automorphic Forms and Geometry of Arithmetic Varieties by K. Hashimoto,Y. Namikawa Pdf

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.

Author : Ze-Li Dou,Qiao Zhang
Publisher : Springer Science & Business Media
Page : 131 pages
File Size : 50,6 Mb
Release : 2012-12-15
Category : Mathematics
ISBN : 9783642287084

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Six Short Chapters on Automorphic Forms and L-functions by Ze-Li Dou,Qiao Zhang Pdf

"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.

Author : Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 55,6 Mb
Release : 2007-10-10
Category : Mathematics
ISBN : 9780817646462

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Representation Theory and Automorphic Forms by Toshiyuki Kobayashi,Wilfried Schmid,Jae-Hyun Yang Pdf

This volume uses a unified approach to representation theory and automorphic forms. It collects papers, written by leading mathematicians, that track recent progress in the expanding fields of representation theory and automorphic forms and their association with number theory and differential geometry. Topics include: Automorphic forms and distributions, modular forms, visible-actions, Dirac cohomology, holomorphic forms, harmonic analysis, self-dual representations, and Langlands Functoriality Conjecture, Both graduate students and researchers will find inspiration in this volume.

Author : Yoshinori Hamahata
Publisher : World Scientific
Page : 388 pages
File Size : 49,8 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814355605

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Geometry and Analysis of Automorphic Forms of Several Variables by Yoshinori Hamahata Pdf

This volume contains contributions of principal speakers of the symposium on geometry and analysis of automorphic forms of several variables, held in September 2009 at Tokyo, Japan, in honor of Takayuki Oda''s 60th birthday. It presents both research and survey articles in the fields that are the main themes of his work. The volume may serve as a guide to developing areas as well as a resource for researchers who seek a broader view and for students who are beginning to explore automorphic form.

Author : James W. Cogdell,Freydoon Shahidi,David Soudry
Publisher : American Mathematical Soc.
Page : 454 pages
File Size : 48,8 Mb
Release : 2014-04-01
Category : Mathematics
ISBN : 9780821893944

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Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro by James W. Cogdell,Freydoon Shahidi,David Soudry Pdf

This volume contains the proceedings of the conference Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro, held from April 23-27, 2012, at Yale University, New Haven, CT. Ilya I. Piatetski-Shapiro, who passed away on 21 February 2009, was a leading figure in the theory of automorphic forms. The conference attempted both to summarize and consolidate the progress that was made during Piatetski-Shapiro's lifetime by him and a substantial group of his co-workers, and to promote future work by identifying fruitful directions of further investigation. It was organized around several themes that reflected Piatetski-Shapiro's main foci of work and that have promise for future development: functoriality and converse theorems; local and global -functions and their periods; -adic -functions and arithmetic geometry; complex geometry; and analytic number theory. In each area, there were talks to review the current state of affairs with special attention to Piatetski-Shapiro's contributions, and other talks to report on current work and to outline promising avenues for continued progress. The contents of this volume reflect most of the talks that were presented at the conference as well as a few additional contributions. They all represent various aspects of the legacy of Piatetski-Shapiro.

Author : Henryk Iwaniec
Publisher : American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
Page : 220 pages
File Size : 41,8 Mb
Release : 2021-11-17
Category : Mathematics
ISBN : 9781470466220

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Spectral Methods of Automorphic Forms by Henryk Iwaniec Pdf

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.

Author : Stephen S. Gelbart
Publisher : Princeton University Press
Page : 284 pages
File Size : 52,6 Mb
Release : 1975-03-21
Category : Mathematics
ISBN : 0691081565

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Automorphic Forms on Adele Groups by Stephen S. Gelbart Pdf

This volume investigates the interplay between the classical theory of automorphic forms and the modern theory of representations of adele groups. Interpreting important recent contributions of Jacquet and Langlands, the author presents new and previously inaccessible results, and systematically develops explicit consequences and connections with the classical theory. The underlying theme is the decomposition of the regular representation of the adele group of GL(2). A detailed proof of the celebrated trace formula of Selberg is included, with a discussion of the possible range of applicability of this formula. Throughout the work the author emphasizes new examples and problems that remain open within the general theory. TABLE OF CONTENTS: 1. The Classical Theory 2. Automorphic Forms and the Decomposition of L2(PSL(2,R) 3. Automorphic Forms as Functions on the Adele Group of GL(2) 4. The Representations of GL(2) over Local and Global Fields 5. Cusp Forms and Representations of the Adele Group of GL(2) 6. Hecke Theory for GL(2) 7. The Construction of a Special Class of Automorphic Forms 8. Eisenstein Series and the Continuous Spectrum 9. The Trace Formula for GL(2) 10. Automorphic Forms on a Quaternion Algebr?

Author : Roger Howe,Jian-Shu Li
Publisher : World Scientific
Page : 446 pages
File Size : 51,6 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770790

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Harmonic Analysis, Group Representations, Automorphic Forms, and Invariant Theory by Roger Howe,Jian-Shu Li Pdf

This volume carries the same title as that of an international conference held at the National University of Singapore, 9OCo11 January 2006 on the occasion of Roger E. Howe''s 60th birthday. Authored by leading members of the Lie theory community, these contributions, expanded from invited lectures given at the conference, are a fitting tribute to the originality, depth and influence of Howe''s mathematical work. The range and diversity of the topics will appeal to a broad audience of research mathematicians and graduate students interested in symmetry and its profound applications. Sample Chapter(s). Foreword (21 KB). Chapter 1: The Theta Correspondence Over R (342 KB). Contents: The Theta Correspondence over R (J Adams); The Heisenberg Group, SL (3, R), and Rigidity (A iap et al.); Pfaffians and Strategies for Integer Choice Games (R Evans & N Wallach); When is an L -Function Non-Vanishing in Part of the Critical Strip? (S Gelbart); Cohomological Automorphic Forms on Unitary Groups, II: Period Relations and Values of L -Functions (M Harris); The Inversion Formula and Holomorphic Extension of the Minimal Representation of the Conformal Group (T Kobayashi & G Mano); Classification des S(r)ries Discr tes pour Certains Groupes Classiques p- Adiques (C Moeglin); Some Algebras of Essentially Compact Distributions of a Reductive p -Adic Group (A Moy & M Tadic); Annihilators of Generalized Verma Modules of the Scalar Type for Classical Lie Algebras (T Oshima); Branching to a Maximal Compact Subgroup (D A Vogan, Jr.); Small Semisimple Subalgebras of Semisimple Lie Algebras (J F Willenbring & G J Zuckerman). Readership: Graduate students and research mathematicians in harmonic analysis, group representations, automorphic forms and invariant theory."

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 42,8 Mb
Release : 2024-07-02
Category : Electronic
ISBN : 9789814474405

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Harmonic Analysis, Group Representations, Automorphic Forms and Invariant Theory by Anonim Pdf