Contributions To Automorphic Forms Geometry And Number Theory

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Contributions to Automorphic Forms, Geometry, and Number Theory

Author : Haruzo Hida
Publisher : JHU Press
ISBN 13 : 9780801878602
Total Pages : 946 pages
Book Rating : 4.8/5 (786 download)

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Book Synopsis Contributions to Automorphic Forms, Geometry, and Number Theory by : Haruzo Hida

Download or read book Contributions to Automorphic Forms, Geometry, and Number Theory written by Haruzo Hida and published by JHU Press. This book was released on 2004-03-11 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Contributions to automorphic forms, geometry, and number theory

Author : Haruzo Hida
Publisher :
ISBN 13 :
Total Pages : 910 pages
Book Rating : 4.:/5 (17 download)

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Book Synopsis Contributions to automorphic forms, geometry, and number theory by : Haruzo Hida

Download or read book Contributions to automorphic forms, geometry, and number theory written by Haruzo Hida and published by . This book was released on 2004 with total page 910 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Number Theory and Modular Forms

Author : Bruce C. Berndt
Publisher : Springer Science & Business Media
ISBN 13 : 1475760442
Total Pages : 392 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Number Theory and Modular Forms by : Bruce C. Berndt

Download or read book Number Theory and Modular Forms written by Bruce C. Berndt and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

L-Functions and Automorphic Forms

Author : Jan Hendrik Bruinier
Publisher : Springer
ISBN 13 : 3319697129
Total Pages : 366 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis L-Functions and Automorphic Forms by : Jan Hendrik Bruinier

Download or read book L-Functions and Automorphic Forms written by Jan Hendrik Bruinier and published by Springer. This book was released on 2018-02-22 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representation Theory and Automorphic Forms

Author : Toshiyuki Kobayashi
Publisher : Springer Science & Business Media
ISBN 13 : 0817646469
Total Pages : 220 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Representation Theory and Automorphic Forms by : Toshiyuki Kobayashi

Download or read book Representation Theory and Automorphic Forms written by Toshiyuki Kobayashi and published by Springer Science & Business Media. This book was released on 2007-10-10 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representation Theory and Automorphic Forms

Author : Toshiyuki Kobayashi
Publisher : Birkhäuser
ISBN 13 : 9780817671297
Total Pages : 214 pages
Book Rating : 4.6/5 (712 download)

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Book Synopsis Representation Theory and Automorphic Forms by : Toshiyuki Kobayashi

Download or read book Representation Theory and Automorphic Forms written by Toshiyuki Kobayashi and published by Birkhäuser. This book was released on 2008-11-01 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Six Short Chapters on Automorphic Forms and L-functions

Author : Ze-Li Dou
Publisher : Springer Science & Business Media
ISBN 13 : 3642287085
Total Pages : 123 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Six Short Chapters on Automorphic Forms and L-functions by : Ze-Li Dou

Download or read book Six Short Chapters on Automorphic Forms and L-functions written by Ze-Li Dou and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Contributions in Analytic and Algebraic Number Theory

Author : Valentin Blomer
Publisher : Springer Science & Business Media
ISBN 13 : 1461412196
Total Pages : 301 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Contributions in Analytic and Algebraic Number Theory by : Valentin Blomer

Download or read book Contributions in Analytic and Algebraic Number Theory written by Valentin Blomer and published by Springer Science & Business Media. This book was released on 2011-11-19 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Spectral Methods of Automorphic Forms

Author : Henryk Iwaniec
Publisher : American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
ISBN 13 : 1470466228
Total Pages : 220 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Spectral Methods of Automorphic Forms by : Henryk Iwaniec

Download or read book Spectral Methods of Automorphic Forms written by Henryk Iwaniec and published by American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain. This book was released on 2021-11-17 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Automorphic Forms and Geometry of Arithmetic Varieties

Author : K. Hashimoto
Publisher : Academic Press
ISBN 13 : 1483218074
Total Pages : 570 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Automorphic Forms and Geometry of Arithmetic Varieties by : K. Hashimoto

Download or read book Automorphic Forms and Geometry of Arithmetic Varieties written by K. Hashimoto and published by Academic Press. This book was released on 2014-07-14 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro

Author : James W. Cogdell
Publisher : American Mathematical Soc.
ISBN 13 : 0821893947
Total Pages : 454 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro by : James W. Cogdell

Download or read book Automorphic Forms and Related Geometry: Assessing the Legacy of I.I. Piatetski-Shapiro written by James W. Cogdell and published by American Mathematical Soc.. This book was released on 2014-04-01 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory

Author : Bretton Woods Workshop on Multiple Dirichlet Series
Publisher : American Mathematical Soc.
ISBN 13 : 0821839632
Total Pages : 320 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory by : Bretton Woods Workshop on Multiple Dirichlet Series

Download or read book Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory written by Bretton Woods Workshop on Multiple Dirichlet Series and published by American Mathematical Soc.. This book was released on 2006 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Dirichlet series are Dirichlet series in several complex variables. A multiple Dirichlet series is said to be perfect if it satisfies a finite group of functional equations and has meromorphic continuation everywhere. The earliest examples came from Mellin transforms of metaplectic Eisenstein series and have been intensively studied over the last twenty years. More recently, many other examples have been discovered and it appears that all the classical theorems on moments of $L$-functions as well as the conjectures (such as those predicted by random matrix theory) can now be obtained via the theory of multiple Dirichlet series. Furthermore, new results, not obtainable by other methods, are just coming to light. This volume offers an account of some of the major research to date and the opportunities for the future. It includes an exposition of the main results in the theory of multiple Dirichlet series, and papers on moments of zeta- and $L$-functions, on new examples of multiple Dirichlet

Automorphic Forms and Galois Representations: Volume 1

Author : Fred Diamond
Publisher : Cambridge University Press
ISBN 13 : 1316062333
Total Pages : 385 pages
Book Rating : 4.3/5 (16 download)

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Book Synopsis Automorphic Forms and Galois Representations: Volume 1 by : Fred Diamond

Download or read book Automorphic Forms and Galois Representations: Volume 1 written by Fred Diamond and published by Cambridge University Press. This book was released on 2014-10-16 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: Automorphic forms and Galois representations have played a central role in the development of modern number theory, with the former coming to prominence via the celebrated Langlands program and Wiles' proof of Fermat's Last Theorem. This two-volume collection arose from the 94th LMS-EPSRC Durham Symposium on 'Automorphic Forms and Galois Representations' in July 2011, the aim of which was to explore recent developments in this area. The expository articles and research papers across the two volumes reflect recent interest in p-adic methods in number theory and representation theory, as well as recent progress on topics from anabelian geometry to p-adic Hodge theory and the Langlands program. The topics covered in volume one include the Shafarevich Conjecture, effective local Langlands correspondence, p-adic L-functions, the fundamental lemma, and other topics of contemporary interest.

Geometry and Analysis of Automorphic Forms of Several Variables

Author : Yoshinori Hamahata
Publisher : World Scientific
ISBN 13 : 9814355607
Total Pages : 388 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Geometry and Analysis of Automorphic Forms of Several Variables by : Yoshinori Hamahata

Download or read book Geometry and Analysis of Automorphic Forms of Several Variables written by Yoshinori Hamahata and published by World Scientific. This book was released on 2012 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modular And Automorphic Forms & Beyond

Author : Hossein Movasati
Publisher : World Scientific
ISBN 13 : 9811238693
Total Pages : 323 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Modular And Automorphic Forms & Beyond by : Hossein Movasati

Download or read book Modular And Automorphic Forms & Beyond written by Hossein Movasati and published by World Scientific. This book was released on 2021-10-12 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: The guiding principle in this monograph is to develop a new theory of modular forms which encompasses most of the available theory of modular forms in the literature, such as those for congruence groups, Siegel and Hilbert modular forms, many types of automorphic forms on Hermitian symmetric domains, Calabi-Yau modular forms, with its examples such as Yukawa couplings and topological string partition functions, and even go beyond all these cases. Its main ingredient is the so-called 'Gauss-Manin connection in disguise'.

Advances in the Theory of Automorphic Forms and Their L-functions

Author : Dihua Jiang
Publisher :
ISBN 13 : 9781470430054
Total Pages : 376 pages
Book Rating : 4.4/5 (3 download)

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Book Synopsis Advances in the Theory of Automorphic Forms and Their L-functions by : Dihua Jiang

Download or read book Advances in the Theory of Automorphic Forms and Their L-functions written by Dihua Jiang and published by . This book was released on 2016 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Arithmetic Geometry and Number Theory

Author : Lin Weng
Publisher : World Scientific
ISBN 13 : 981256814X
Total Pages : 411 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Arithmetic Geometry and Number Theory by : Lin Weng

Download or read book Arithmetic Geometry and Number Theory written by Lin Weng and published by World Scientific. This book was released on 2006 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is very much a part of our culture; and this invaluable collection serves the purpose of developing the branches involved, popularizing the existing theories and guiding our future explorations.More precisely, the goal is to bring the reader to the frontier of current developments in arithmetic geometry and number theory through the works of Deninger-Werner in vector bundles on curves over p-adic fields; of Jiang on local gamma factors in automorphic representations; of Weng on Deligne pairings and Takhtajan-Zograf metrics; of Yoshida on CM-periods; of Yu on transcendence of special values of zetas over finite fields. In addition, the lecture notes presented by Weng at the University of Toronto from October to November 2005 explain basic ideas and the reasons (not just the language and conclusions) behind Langlands' fundamental, yet notably difficult, works on the Eisenstein series and spectral decompositions.And finally, a brand new concept by Weng called the Geometric Arithmetic program that uses algebraic and/or analytic methods, based on geometric considerations, to develop the promising and yet to be cultivated land of global arithmetic that includes non-abelian Class Field Theory, Riemann Hypothesis and non-abelian Zeta and L Functions, etc.