Rankin Selberg Convolutions For So 2 1gl N Local Theory

Author : David Soudry
Publisher : American Mathematical Soc.
Page : 100 pages
File Size : 52,5 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821825686

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Rankin-Selberg Convolutions for SO_2+1GL_n : Local Theory by David Soudry Pdf

This work studies the local theory for certain Rankin-Selberg convolutions for the standard $L$-function of degree $21n$ of generic representations of $\textnormal{SO}_{2\ell +1}(F)\times \textnormal{GL}_n(F)$ over a local field $F$. The local integrals converge in a half-plane and continue meromorphically to the whole plane. One main result is the existence of local gamma and $L$-factors. The gamma factor is obtained as a proportionality factor of a functional equation satisfied by the local integrals. In addition, Soudry establishes the multiplicativity of the gamma factor ($1

Author : Henryk Iwaniec,Emmanuel Kowalski
Publisher : American Mathematical Soc.
Page : 615 pages
File Size : 48,6 Mb
Release : 2021-10-14
Category : Education
ISBN : 9781470467708

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Analytic Number Theory by Henryk Iwaniec,Emmanuel Kowalski Pdf

Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results. One of the primary attractions of this theory is its vast diversity of concepts and methods. The main goals of this book are to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, beautiful theorems, and powerful techniques. The book is written with graduate students in mind, and the authors nicely balance clarity, completeness, and generality. The exercises in each section serve dual purposes, some intended to improve readers' understanding of the subject and others providing additional information. Formal prerequisites for the major part of the book do not go beyond calculus, complex analysis, integration, and Fourier series and integrals. In later chapters automorphic forms become important, with much of the necessary information about them included in two survey chapters.

Author : Anonim
Publisher : American Mathematical Society(RI)
Page : 1084 pages
File Size : 45,6 Mb
Release : 1997
Category : Number theory
ISBN : UCAL:B5102240

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Reviews in Number Theory, 1984-96 by Anonim Pdf

These six volumes include approximately 20,000 reviews of items in number theory that appeared in Mathematical Reviews (MR) between 1984 and 1996. This is the third such set of volumes in number theory: the first was edited by W.J. LeVeque and included reviews from 1940-1972; the second was edited by R.K. Guy and appeared in 1984.

Author : Anonim
Publisher : Unknown
Page : 636 pages
File Size : 49,6 Mb
Release : 1993
Category : Mathematics
ISBN : UOM:39015051367392

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Mathematical Reviews by Anonim Pdf

Author : Haruzo Hida
Publisher : Cambridge University Press
Page : 404 pages
File Size : 45,5 Mb
Release : 1993-02-11
Category : Mathematics
ISBN : 0521435692

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Elementary Theory of L-functions and Eisenstein Series by Haruzo Hida Pdf

The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.

Author : Stefan Patrikis
Publisher : American Mathematical Soc.
Page : 156 pages
File Size : 43,6 Mb
Release : 2019-04-10
Category : Algebraic number theory
ISBN : 9781470435400

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Variations on a Theorem of Tate by Stefan Patrikis Pdf

Let F be a number field. These notes explore Galois-theoretic, automorphic, and motivic analogues and refinements of Tate's basic result that continuous projective representations Gal(F¯¯¯¯/F)→PGLn(C) lift to GLn(C). The author takes special interest in the interaction of this result with algebraicity (for automorphic representations) and geometricity (in the sense of Fontaine-Mazur). On the motivic side, the author studies refinements and generalizations of the classical Kuga-Satake construction. Some auxiliary results touch on: possible infinity-types of algebraic automorphic representations; comparison of the automorphic and Galois “Tannakian formalisms” monodromy (independence-of-ℓ) questions for abstract Galois representations.

Author : Wen-Wei Li
Publisher : Springer
Page : 148 pages
File Size : 44,7 Mb
Release : 2018-11-02
Category : Mathematics
ISBN : 9783030012885

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Zeta Integrals, Schwartz Spaces and Local Functional Equations by Wen-Wei Li Pdf

This book focuses on a conjectural class of zeta integrals which arose from a program born in the work of Braverman and Kazhdan around the year 2000, the eventual goal being to prove the analytic continuation and functional equation of automorphic L-functions. Developing a general framework that could accommodate Schwartz spaces and the corresponding zeta integrals, the author establishes a formalism, states desiderata and conjectures, draws implications from these assumptions, and shows how known examples fit into this framework, supporting Sakellaridis' vision of the subject. The collected results, both old and new, and the included extensive bibliography, will be valuable to anyone who wishes to understand this program, and to those who are already working on it and want to overcome certain frequently occurring technical difficulties.

Author : Paul Garrett
Publisher : Cambridge University Press
Page : 407 pages
File Size : 52,6 Mb
Release : 2018-09-20
Category : Mathematics
ISBN : 9781107154001

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Modern Analysis of Automorphic Forms By Example by Paul Garrett Pdf

Volume 1 of a two-volume introduction to the analytical aspects of automorphic forms, featuring proofs of critical results with examples.

Author : Clay Mathematics Institute. Summer School
Publisher : American Mathematical Soc.
Page : 708 pages
File Size : 41,7 Mb
Release : 2005
Category : Mathematics
ISBN : 082183844X

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Harmonic Analysis, the Trace Formula, and Shimura Varieties by Clay Mathematics Institute. Summer School Pdf

Langlands program proposes fundamental relations that tie arithmetic information from number theory and algebraic geometry with analytic information from harmonic analysis and group representations. This title intends to provide an entry point into this exciting and challenging field.

Author : James Arthur,Laurent Clozel
Publisher : Princeton University Press
Page : 252 pages
File Size : 44,6 Mb
Release : 1989-06-21
Category : Mathematics
ISBN : 0691085188

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Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula by James Arthur,Laurent Clozel Pdf

A general principle, discovered by Robert Langlands and named by him the "functoriality principle," predicts relations between automorphic forms on arithmetic subgroups of different reductive groups. Langlands functoriality relates the eigenvalues of Hecke operators acting on the automorphic forms on two groups (or the local factors of the "automorphic representations" generated by them). In the few instances where such relations have been probed, they have led to deep arithmetic consequences. This book studies one of the simplest general problems in the theory, that of relating automorphic forms on arithmetic subgroups of GL(n,E) and GL(n,F) when E/F is a cyclic extension of number fields. (This is known as the base change problem for GL(n).) The problem is attacked and solved by means of the trace formula. The book relies on deep and technical results obtained by several authors during the last twenty years. It could not serve as an introduction to them, but, by giving complete references to the published literature, the authors have made the work useful to a reader who does not know all the aspects of the theory of automorphic forms.

Author : Richard Crandall,Carl B. Pomerance
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 54,8 Mb
Release : 2006-04-07
Category : Mathematics
ISBN : 9780387289793

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Prime Numbers by Richard Crandall,Carl B. Pomerance Pdf

Bridges the gap between theoretical and computational aspects of prime numbers Exercise sections are a goldmine of interesting examples, pointers to the literature and potential research projects Authors are well-known and highly-regarded in the field

Author : Martin Eichler,Don Zagier
Publisher : Springer Science & Business Media
Page : 150 pages
File Size : 45,8 Mb
Release : 2013-12-14
Category : Mathematics
ISBN : 9781468491623

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The Theory of Jacobi Forms by Martin Eichler,Don Zagier Pdf

The functions studied in this monogra9h are a cross between elliptic functions and modular forms in one variable. Specifically, we define a Jacobi form on SL (~) to be a holomorphic function 2 (JC = upper half-plane) satisfying the t\-10 transformation eouations 2Tiimcz· k CT +d a-r +b z) (1) ((cT+d) e cp(T, z) cp CT +d ' CT +d (2) rjl(T, z+h+]l) and having a Four·ier expansion of the form 00 e2Tii(nT +rz) (3) cp(T, z) 2: c(n, r) 2:: rE~ n=O 2 r ~ 4nm Here k and m are natural numbers, called the weight and index of rp, respectively. Note that th e function cp (T, 0) is an ordinary modular formofweight k, whileforfixed T thefunction z-+rjl( -r, z) isa function of the type normally used to embed the elliptic curve ~/~T + ~ into a projective space. If m= 0, then cp is independent of z and the definition reduces to the usual notion of modular forms in one variable. We give three other examples of situations where functions satisfying (1)-(3) arise classically: 1. Theta series. Let Q: ~-+ ~ be a positive definite integer valued quadratic form and B the associated bilinear form.

Author : Freydoon Shahidi
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 42,6 Mb
Release : 2010
Category : Mathematics
ISBN : 9780821849897

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Eisenstein Series and Automorphic $L$-Functions by Freydoon Shahidi Pdf

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.

Author : Jayce Getz,Mark Goresky
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 48,6 Mb
Release : 2012-03-28
Category : Mathematics
ISBN : 9783034803519

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Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change by Jayce Getz,Mark Goresky Pdf

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

Author : Wee Teck Gan,Stephen S. Kudla,Yuri Tschinkel
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 50,9 Mb
Release : 2007-12-22
Category : Mathematics
ISBN : 9780817646394

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Eisenstein Series and Applications by Wee Teck Gan,Stephen S. Kudla,Yuri Tschinkel Pdf

Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. They have also been exploited extensively by number theorists for many arithmetic purposes. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications. With this juxtaposition of perspectives, the reader obtains deeper insights into the arithmetic of Eisenstein series. The central theme of the exposition focuses on the common structural properties of Eisenstein series occurring in many related applications.