Advances In The Theory Of Automorphic Forms And Their L Functions

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Automorphic Forms and L-Functions for the Group GL(n,R)

Author : Dorian Goldfeld
Publisher : Cambridge University Press
ISBN 13 : 1139456202
Total Pages : 65 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Automorphic Forms and L-Functions for the Group GL(n,R) by : Dorian Goldfeld

Download or read book Automorphic Forms and L-Functions for the Group GL(n,R) written by Dorian Goldfeld and published by Cambridge University Press. This book was released on 2006-08-03 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: L-functions associated to automorphic forms encode all classical number theoretic information. They are akin to elementary particles in physics. This book provides an entirely self-contained introduction to the theory of L-functions in a style accessible to graduate students with a basic knowledge of classical analysis, complex variable theory, and algebra. Also within the volume are many new results not yet found in the literature. The exposition provides complete detailed proofs of results in an easy-to-read format using many examples and without the need to know and remember many complex definitions. The main themes of the book are first worked out for GL(2,R) and GL(3,R), and then for the general case of GL(n,R). In an appendix to the book, a set of Mathematica functions is presented, designed to allow the reader to explore the theory from a computational point of view.

Multiple Dirichlet Series, L-functions and Automorphic Forms

Author : Daniel Bump
Publisher : Springer
ISBN 13 : 0817683348
Total Pages : 367 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Multiple Dirichlet Series, L-functions and Automorphic Forms by : Daniel Bump

Download or read book Multiple Dirichlet Series, L-functions and Automorphic Forms written by Daniel Bump and published by Springer. This book was released on 2012-07-09 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Dirichlet Series, L-functions and Automorphic Forms gives the latest advances in the rapidly developing subject of Multiple Dirichlet Series, an area with origins in the theory of automorphic forms that exhibits surprising and deep connections to crystal graphs and mathematical physics. As such, it represents a new way in which areas including number theory, combinatorics, statistical mechanics, and quantum groups are seen to fit together. The volume also includes papers on automorphic forms and L-functions and related number-theoretic topics. This volume will be a valuable resource for graduate students and researchers in number theory, combinatorics, representation theory, mathematical physics, and special functions. Contributors: J. Beineke, B. Brubaker, D. Bump, G. Chinta, G. Cornelissen, C.A. Diaconu, S. Frechette, S. Friedberg, P. Garrett, D. Goldfeld, P.E. Gunnells, B. Heim, J. Hundley, D. Ivanov, Y. Komori, A.V. Kontorovich, O. Lorscheid, K. Matsumoto, P.J. McNamara, S.J. Patterson, M. Suzuki, H. Tsumura.

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

Author : Dihua Jiang
Publisher : American Mathematical Soc.
ISBN 13 : 147041709X
Total Pages : 386 pages
Book Rating : 4.4/5 (74 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 American Mathematical Soc.. This book was released on 2016-04-29 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the workshop on “Advances in the Theory of Automorphic Forms and Their L-functions” held in honor of James Cogdell's 60th birthday, held from October 16–25, 2013, at the Erwin Schrödinger Institute (ESI) at the University of Vienna. The workshop and the papers contributed to this volume circle around such topics as the theory of automorphic forms and their L-functions, geometry and number theory, covering some of the recent approaches and advances to these subjects. Specifically, the papers cover aspects of representation theory of p-adic groups, classification of automorphic representations through their Fourier coefficients and their liftings, L-functions for classical groups, special values of L-functions, Howe duality, subconvexity for L-functions, Kloosterman integrals, arithmetic geometry and cohomology of arithmetic groups, and other important problems on L-functions, nodal sets and geometry.

Automorphic Forms on GL (3,TR)

Author : D. Bump
Publisher : Springer
ISBN 13 : 3540390553
Total Pages : 196 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Automorphic Forms on GL (3,TR) by : D. Bump

Download or read book Automorphic Forms on GL (3,TR) written by D. Bump and published by Springer. This book was released on 2006-12-08 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Curves, Modular Forms, and Their L-functions

Author : Álvaro Lozano-Robledo
Publisher : American Mathematical Soc.
ISBN 13 : 0821852426
Total Pages : 217 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Elliptic Curves, Modular Forms, and Their L-functions by : Álvaro Lozano-Robledo

Download or read book Elliptic Curves, Modular Forms, and Their L-functions written by Álvaro Lozano-Robledo and published by American Mathematical Soc.. This book was released on 2011 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in number theory have simple statements, but their solutions require a deep understanding of algebra, algebraic geometry, complex analysis, group representations, or a combination of all four. The original simply stated problem can be obscured in the depth of the theory developed to understand it. This book is an introduction to some of these problems, and an overview of the theories used nowadays to attack them, presented so that the number theory is always at the forefront of the discussion. Lozano-Robledo gives an introductory survey of elliptic curves, modular forms, and $L$-functions. His main goal is to provide the reader with the big picture of the surprising connections among these three families of mathematical objects and their meaning for number theory. As a case in point, Lozano-Robledo explains the modularity theorem and its famous consequence, Fermat's Last Theorem. He also discusses the Birch and Swinnerton-Dyer Conjecture and other modern conjectures. The book begins with some motivating problems and includes numerous concrete examples throughout the text, often involving actual numbers, such as 3, 4, 5, $\frac{3344161}{747348}$, and $\frac{2244035177043369699245575130906674863160948472041} {8912332268928859588025535178967163570016480830}$. The theories of elliptic curves, modular forms, and $L$-functions are too vast to be covered in a single volume, and their proofs are outside the scope of the undergraduate curriculum. However, the primary objects of study, the statements of the main theorems, and their corollaries are within the grasp of advanced undergraduates. This book concentrates on motivating the definitions, explaining the statements of the theorems and conjectures, making connections, and providing lots of examples, rather than dwelling on the hard proofs. The book succeeds if, after reading the text, students feel compelled to study elliptic curves and modular forms in all their glory.

Automorphic Forms, Representations and $L$-Functions

Author : Armand Borel
Publisher : American Mathematical Soc.
ISBN 13 : 0821814370
Total Pages : 394 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Automorphic Forms, Representations and $L$-Functions by : Armand Borel

Download or read book Automorphic Forms, Representations and $L$-Functions written by Armand Borel and published by American Mathematical Soc.. This book was released on 1979-06-30 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part 2 contains sections on Automorphic representations and $L$-functions, Arithmetical algebraic geometry and $L$-functions

Automorphic Forms on GL (2)

Author : H. Jacquet
Publisher : Springer
ISBN 13 : 3540376127
Total Pages : 156 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Automorphic Forms on GL (2) by : H. Jacquet

Download or read book Automorphic Forms on GL (2) written by H. Jacquet and published by Springer. This book was released on 2006-11-15 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Topics in Classical Automorphic Forms

Author : Henryk Iwaniec
Publisher : American Mathematical Soc.
ISBN 13 : 0821807773
Total Pages : 274 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topics in Classical Automorphic Forms by : Henryk Iwaniec

Download or read book Topics in Classical Automorphic Forms written by Henryk Iwaniec and published by American Mathematical Soc.. This book was released on 1997 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Eisenstein Series and Automorphic $L$-Functions

Author : Freydoon Shahidi
Publisher : American Mathematical Soc.
ISBN 13 : 0821849891
Total Pages : 218 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Eisenstein Series and Automorphic $L$-Functions by : Freydoon Shahidi

Download or read book Eisenstein Series and Automorphic $L$-Functions written by Freydoon Shahidi and published by American Mathematical Soc.. This book was released on 2010 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a treatment of the theory of $L$-functions developed by means of the theory of Eisenstein series and their Fourier coefficients, a theory which is usually referred to as the Langlands-Shahidi method. The information gathered from this method, when combined with the converse theorems of Cogdell and Piatetski-Shapiro, has been quite sufficient in establishing a number of new cases of Langlands functoriality conjecture; at present, some of these cases cannot be obtained by any other method. These results have led to far-reaching new estimates for Hecke eigenvalues of Maass forms, as well as definitive solutions to certain problems in analytic and algebraic number theory. This book gives a detailed treatment of important parts of this theory, including a rather complete proof of Casselman-Shalika's formula for unramified Whittaker functions as well as a general treatment of the theory of intertwining operators. It also covers in some detail the global aspects of the method as well as some of its applications to group representations and harmonic analysis. This book is addressed to graduate students and researchers who are interested in the Langlands program in automorphic forms and its connections with number theory.

Families of Automorphic Forms and the Trace Formula

Author : Werner Müller
Publisher : Springer
ISBN 13 : 3319414240
Total Pages : 581 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Families of Automorphic Forms and the Trace Formula by : Werner Müller

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.

Automorphic Forms

Author : Anton Deitmar
Publisher : Springer Science & Business Media
ISBN 13 : 144714435X
Total Pages : 255 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Automorphic Forms by : Anton Deitmar

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.

Automorphic Forms and Applications

Author : Peter Sarnak
Publisher : American Mathematical Soc.
ISBN 13 : 0821828738
Total Pages : 443 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Automorphic Forms and Applications by : Peter Sarnak

Download or read book Automorphic Forms and Applications written by Peter Sarnak and published by American Mathematical Soc.. This book was released on 2007 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of automorphic forms has seen dramatic developments in recent years. In particular, important instances of Langlands functoriality have been established. This volume presents three weeks of lectures from the IAS/Park City Mathematics Institute Summer School on automorphic forms and their applications. It addresses some of the general aspects of automorphic forms, as well as certain recent advances in the field. The book starts with the lectures of Borel on the basic theory of automorphic forms, which lay the foundation for the lectures by Cogdell and Shahidi on converse theorems and the Langlands-Shahidi method, as well as those by Clozel and Li on the Ramanujan conjectures and graphs. The analytic theory of GL(2)-forms and $L$-functions are the subject of Michel's lectures, while Terras covers arithmetic quantum chaos. The volume also includes a chapter by Vogan on isolated unitary representations, which is related to the lectures by Clozel. This volume is recommended for independent study or an advanced topics course. It is suitable for graduate students and researchers interested in automorphic forms and number theory. the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Eisenstein Series and Automorphic Representations

Author : Philipp Fleig
Publisher : Cambridge Studies in Advanced
ISBN 13 : 1107189926
Total Pages : 587 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Eisenstein Series and Automorphic Representations by : Philipp Fleig

Download or read book Eisenstein Series and Automorphic Representations written by Philipp Fleig and published by Cambridge Studies in Advanced. This book was released on 2018-07-05 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.

Advanced Analytic Number Theory: L-Functions

Author : Carlos J. Moreno
Publisher : American Mathematical Soc.
ISBN 13 : 0821842668
Total Pages : 313 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advanced Analytic Number Theory: L-Functions by : Carlos J. Moreno

Download or read book Advanced Analytic Number Theory: L-Functions written by Carlos J. Moreno and published by American Mathematical Soc.. This book was released on 2005 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering work of Euler, Dirichlet, and Riemann, the analytic properties of L-functions have been used to study the distribution of prime numbers. With the advent of the Langlands Program, L-functions have assumed a greater role in the study of the interplay between Diophantine questions about primes and representation theoretic properties of Galois representations. This book provides a complete introduction to the most significant class of L-functions: the Artin-Hecke L-functions associated to finite-dimensional representations of Weil groups and to automorphic L-functions of principal type on the general linear group. In addition to establishing functional equations, growth estimates, and non-vanishing theorems, a thorough presentation of the explicit formulas of Riemann type in the context of Artin-Hecke and automorphic L-functions is also given. The survey is aimed at mathematicians and graduate students who want to learn about the modern analytic theory of L-functions and their applications in number theory and in the theory of automorphic representations. The requirements for a profitable study of this monograph are a knowledge of basic number theory and the rudiments of abstract harmonic analysis on locally compact abelian groups.

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.

p-Adic Automorphic Forms on Shimura Varieties

Author : Haruzo Hida
Publisher : Springer Science & Business Media
ISBN 13 : 9780387207117
Total Pages : 414 pages
Book Rating : 4.2/5 (71 download)

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Book Synopsis p-Adic Automorphic Forms on Shimura Varieties by : Haruzo Hida

Download or read book p-Adic Automorphic Forms on Shimura Varieties written by Haruzo Hida and published by Springer Science & Business Media. This book was released on 2004-05-10 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the following three topics in a manner accessible to graduate students who have an understanding of algebraic number theory and scheme theoretic algebraic geometry: 1. An elementary construction of Shimura varieties as moduli of abelian schemes. 2. p-adic deformation theory of automorphic forms on Shimura varieties. 3. A simple proof of irreducibility of the generalized Igusa tower over the Shimura variety. The book starts with a detailed study of elliptic and Hilbert modular forms and reaches to the forefront of research of Shimura varieties associated with general classical groups. The method of constructing p-adic analytic families and the proof of irreducibility was recently discovered by the author. The area covered in this book is now a focal point of research worldwide with many far-reaching applications that have led to solutions of longstanding problems and conjectures. Specifically, the use of p-adic elliptic and Hilbert modular forms have proven essential in recent breakthroughs in number theory (for example, the proof of Fermat's Last Theorem and the Shimura-Taniyama conjecture by A. Wiles and others). Haruzo Hida is Professor of Mathematics at University of California, Los Angeles. His previous books include Modular Forms and Galois Cohomology (Cambridge University Press 2000) and Geometric Modular Forms and Elliptic Curves (World Scientific Publishing Company 2000).