Automorphic Functions And Number Theory

DOWNLOAD

Download Automorphic Functions And Number Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Automorphic Functions And Number Theory book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Introduction To The Arithmetic Theory Of Automorphic Functions

DOWNLOAD
Author : Gorō Shimura
language : en
Publisher: Princeton University Press
Release Date : 1971-08-21

Introduction To The Arithmetic Theory Of Automorphic Functions written by Gorō Shimura and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971-08-21 with Mathematics categories.

The theory of automorphic forms is playing increasingly important roles in several branches of mathematics, even in physics, and is almost ubiquitous in number theory. This book introduces the reader to the subject and in particular to elliptic modular forms with emphasis on their number-theoretical aspects. After two chapters geared toward elementary levels, there follows a detailed treatment of the theory of Hecke operators, which associate zeta functions to modular forms. At a more advanced level, complex multiplication of elliptic curves and abelian varieties is discussed. The main question is the construction of abelian extensions of certain algebraic number fields, which is traditionally called "Hilbert's twelfth problem." Another advanced topic is the determination of the zeta function of an algebraic curve uniformized by modular functions, which supplies an indispensable background for the recent proof of Fermat's last theorem by Wiles.

Automorphic Functions And Number Theory

DOWNLOAD
Author : Goro Shimura
language : en
Publisher: Springer
Release Date : 2006-11-15

Automorphic Functions And Number Theory written by Goro Shimura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Automorphic Forms

DOWNLOAD
Author : Anton Deitmar
language : en
Publisher: Springer
Release Date : 2012-08-29

Automorphic Forms written by Anton Deitmar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.

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 Functions And Number Theory

DOWNLOAD
Author : Gorō Shimura
language : en
Publisher:
Release Date : 1968

Automorphic Functions And Number Theory written by Gorō Shimura and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968 with Automorphic functions categories.

Automorphic Forms And L Functions For The Group Gl N R

DOWNLOAD
Author : Dorian Goldfeld
language : en
Publisher: Cambridge University Press
Release Date : 2015-11-26

Automorphic Forms And L Functions For The Group Gl N R written by Dorian Goldfeld and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-26 with Mathematics categories.

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.

Explicit Constructions Of Automorphic L Functions

DOWNLOAD
Author : Stephen Gelbart
language : en
Publisher: Springer
Release Date : 2006-11-15

Explicit Constructions Of Automorphic L Functions written by Stephen Gelbart and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

The goal of this research monograph is to derive the analytic continuation and functional equation of the L-functions attached by R.P. Langlands to automorphic representations of reductive algebraic groups. The first part of the book (by Piatetski-Shapiro and Rallis) deals with L-functions for the simple classical groups; the second part (by Gelbart and Piatetski-Shapiro) deals with non-simple groups of the form G GL(n), with G a quasi-split reductive group of split rank n. The method of proof is to construct certain explicit zeta-integrals of Rankin-Selberg type which interpolate the relevant Langlands L-functions and can be analyzed via the theory of Eisenstein series and intertwining operators. This is the first time such an approach has been applied to such general classes of groups. The flavor of the local theory is decidedly representation theoretic, and the work should be of interest to researchers in group representation theory as well as number theory.

Contributions To Automorphic Forms Geometry And Number Theory

DOWNLOAD
Author : Haruzo Hida
language : en
Publisher: JHU Press
Release Date : 2004-03-11

Contributions To Automorphic Forms Geometry And Number Theory written by Haruzo Hida and has been published by JHU Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-11 with Mathematics categories.

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.

Automorphic Forms And Applications

DOWNLOAD
Author : Peter Sarnak
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Automorphic Forms And Applications written by Peter Sarnak and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

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.

Modular Functions In Analytic Number Theory

DOWNLOAD
Author : Marvin Isadore Knopp
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Modular Functions In Analytic Number Theory written by Marvin Isadore Knopp and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

Knopp's engaging book presents an introduction to modular functions in number theory by concentrating on two modular functions, $\eta(\tau)$ and $\vartheta(\tau)$, and their applications to two number-theoretic functions, $p(n)$ and $r_s(n)$. They are well chosen, as at the heart of these particular applications to the treatment of these specific number-theoretic functions lies the general theory of automorphic functions, a theory of far-reaching significance with important connections to a great many fields of mathematics. The book is essentially self-contained, assuming only a good first-year course in analysis. The excellent exposition presents the beautiful interplay between modular forms and number theory, making the book an excellent introduction to analytic number theory for a beginning graduate student. Table of Contents: The Modular Group and Certain Subgroups: 1. The modular group; 2. A fundamental region for $\Gamma(1)$; 3. Some subgroups of $\Gamma(1)$; 4. Fundamental regions of subgroups. Modular Functions and Forms: 1. Multiplier systems; 2. Parabolic points; 3 Fourier expansions; 4. Definitions of modular function and modular form; 5. Several important theorems.The Modular Forms $\eta(\tau)$ and $\vartheta(\tau)$: 1. The function $\eta(\tau)$; 2. Several famous identities; 3. Transformation formulas for $\eta(\tau)$; 4. The function $\vartheta(\tau)$. The Multiplier Systems $\upsilon_{\eta}$ and $\upsilon_{\vartheta}$: 1. Preliminaries; 2. Proof of theorem 2; 3. Proof of theorem 3. Sums of Squares: 1. Statement of results; 2. Lipschitz summation formula; 3. The function $\psi_s(\tau)$; 4. The expansion of $\psi_s(\tau)$ at $-1$; 5. Proofs of theorems 2 and 3; 6. Related results. The Order of Magnitude of $p(n)$: 1. A simple inequality for $p(n)$; 2. The asymptotic formula for $p(n)$; 3. Proof of theorem 2. The Ramanujan Congruences for $p(n)$: 1. Statement of the congruences; 2. The functions $\Phi_{p, r}(\tau)$ and $h_p(\tau)$; 3. The function $s_{p, r}(\tau)$; 4. The congruence for $p(n)$ Modulo 11; 5. Newton's formula; 6. The modular equation for the prime 5; 7. The modular equation for the prime 7. Proof of the Ramanujan Congruences for Powers of 5 and 7: 1. Preliminaries; 2. Application of the modular equation; 3. A digression: The Ramanujan identities for powers of the prime 5; 4. Completion of the proof for powers of 5; 5.Start of the proof for powers of 7; 6. A second digression: The Ramanujan identities for powers of the prime 7; 7. Completion of the proof for powers of 7. Index. (CHEL/337.H

Spectral Methods Of Automorphic Forms

DOWNLOAD
Author : Henryk Iwaniec
language : en
Publisher: American Mathematical Soc.
Release Date : 2002

Spectral Methods Of Automorphic Forms written by Henryk Iwaniec and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

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 volume was an underground classic, both as a textbook and as a respected source for results, ideas, and references. The book's reputation sparked a growing interest inthe mathematical community to bring it back into print. The AMS has answered that call with the publication of this second edition. In the book, Iwaniec treats the spectral theory of automorphic forms as the study of the space $L2 (H\Gamma)$, where $H$ is the upper half-plane and $\Gamma$ is a discretesubgroup of volume-preserving transformations of $H$. He combines various techniques from analytic number theory. Among the topics discussed are Eisenstein series, estimates for Fourier coefficients of automorphic forms, the theory of Kloosterman sums, the Selberg trace formula, and the theory of small eigenvalues. Henryk Iwaniec was awarded the 2002 AMS Cole Prize for his fundamental contributions to analytic number theory. Also available from the AMS by H. Iwaniec is Topics in ClassicalAutomorphic Forms, Volume 17 in the Graduate Studies in Mathematics series. The book is designed for graduate students and researchers working in analytic number theory.