Arithmetic Geometry And Automorphic Forms

Author : James W. Cogdell
Publisher : International Pressof Boston Incorporated
ISBN 13 : 9781571462299
Total Pages : 557 pages
Book Rating : 4.95/5 ( download)

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Download or read book Arithmetic Geometry and Automorphic Forms written by James W. Cogdell and published by International Pressof Boston Incorporated. This book was released on 2011 with total page 557 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : K. Hashimoto
Publisher : Academic Press
ISBN 13 : 1483218074
Total Pages : 540 pages
Book Rating : 4.76/5 ( download)

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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 540 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.

Author : Anton Deitmar
Publisher : Springer Science & Business Media
ISBN 13 : 144714435X
Total Pages : 255 pages
Book Rating : 4.59/5 ( download)

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Download or read book Automorphic Forms written by Anton Deitmar and published by Springer Science & Business Media. This book was released on 2012-08-29 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Haruzo Hida
Publisher : JHU Press
ISBN 13 : 9780801878602
Total Pages : 946 pages
Book Rating : 4.08/5 ( download)

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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.

Author : Gary Cornell
Publisher : Springer Science & Business Media
ISBN 13 : 1461219744
Total Pages : 592 pages
Book Rating : 4.43/5 ( download)

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Download or read book Modular Forms and Fermat’s Last Theorem written by Gary Cornell and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the expanded lectures given at a conference on number theory and arithmetic geometry held at Boston University. It introduces and explains the many ideas and techniques used by Wiles, and to explain how his result can be combined with Ribets theorem and ideas of Frey and Serre to prove Fermats Last Theorem. The book begins with an overview of the complete proof, followed by several introductory chapters surveying the basic theory of elliptic curves, modular functions and curves, Galois cohomology, and finite group schemes. Representation theory, which lies at the core of the proof, is dealt with in a chapter on automorphic representations and the Langlands-Tunnell theorem, and this is followed by in-depth discussions of Serres conjectures, Galois deformations, universal deformation rings, Hecke algebras, and complete intersections. The book concludes by looking both forward and backward, reflecting on the history of the problem, while placing Wiles'theorem into a more general Diophantine context suggesting future applications. Students and professional mathematicians alike will find this an indispensable resource.

Author : Werner Müller
Publisher : Springer
ISBN 13 : 3319414240
Total Pages : 581 pages
Book Rating : 4.49/5 ( download)

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Download or read book Families of Automorphic Forms and the Trace Formula written by Werner Müller and published by Springer. This book was released on 2016-09-20 with total page 581 pages. Available in PDF, EPUB and Kindle. Book excerpt: Featuring the work of twenty-three internationally-recognized experts, this volume explores the trace formula, spectra of locally symmetric spaces, p-adic families, and other recent techniques from harmonic analysis and representation theory. Each peer-reviewed submission in this volume, based on the Simons Foundation symposium on families of automorphic forms and the trace formula held in Puerto Rico in January-February 2014, is the product of intensive research collaboration by the participants over the course of the seven-day workshop. The goal of each session in the symposium was to bring together researchers with diverse specialties in order to identify key difficulties as well as fruitful approaches being explored in the field. The respective themes were counting cohomological forms, p-adic trace formulas, Hecke fields, slopes of modular forms, and orbital integrals.

Author : Lin Weng
Publisher : World Scientific
ISBN 13 : 9814477931
Total Pages : 411 pages
Book Rating : 4.32/5 ( download)

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Download or read book Arithmetic Geometry And Number Theory written by Lin Weng and published by World Scientific. This book was released on 2006-06-02 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.

Author : Jean-Pierre Labesse
Publisher : Springer
ISBN 13 : 3540468765
Total Pages : 358 pages
Book Rating : 4.69/5 ( download)

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Download or read book Cohomology of Arithmetic Groups and Automorphic Forms written by Jean-Pierre Labesse and published by Springer. This book was released on 2006-11-14 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of arithmetic groups serves as a tool in studying possible relations between the theory of automorphic forms and the arithmetic of algebraic varieties resp. the geometry of locally symmetric spaces. These proceedings will serve as a guide to this still rapidly developing area of mathematics. Besides two survey articles, the contributions are original research papers.

Author : Jan Hendrik Bruinier
Publisher : Springer
ISBN 13 : 3319697129
Total Pages : 366 pages
Book Rating : 4.23/5 ( download)

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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.

Author : Walter L. Baily Jr.
Publisher : Princeton University Press
ISBN 13 : 1400867150
Total Pages : 279 pages
Book Rating : 4.58/5 ( download)

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Download or read book Introductory Lectures on Automorphic Forms written by Walter L. Baily Jr. and published by Princeton University Press. This book was released on 2015-03-08 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended as an introductory guide, this work takes for its subject complex, analytic, automorphic forms and functions on (a domain equivalent to) a bounded domain in a finite-dimensional, complex, vector space, usually denoted Cn). Part I, essentially elementary, deals with complex analytic automorphic forms on a bounded domain; it presents H. Cartan's proof of the existence of the projective imbedding of the compact quotient of such a domain by a discrete group. Part II treats the construction and properties of automorphic forms with respect to an arithmetic group acting on a bounded symmetric domain; this part is highly technical, and based largely on relevant results in functional analysis due to Godement and Harish-Chandra. In Part III, Professor Baily extends the discussion to include some special topics, specifically, the arithmetic propertics of Eisenstein series and their connection with the arithmetic theory of quadratic forms. Unlike classical works on the subject, this book deals with more than one variable, and it differs notably in its treatment of analysis on the group of automorphisms of the domain. It is concerned with the case of complex analytic automorphic forms because of their connection with algebraic geometry, and so is distinct from other modern treatises that deal with automorphic forms on a semi-simple Lie group. Having had its inception as graduate- level lectures, the book assumes some knowledge of complex function theory and algebra, for the serious reader is expected to supply certain details for himself, especially in such related areas as functional analysis and algebraic groups. Originally published in 1973. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.