The Arithmetic And Spectral Analysis Of Poincaré Series

Author : James W. Cogdell,Iiya Piatetski-Shapiro
Publisher : Academic Press
Page : 190 pages
File Size : 40,5 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781483266176

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The Arithmetic and Spectral Analysis of Poincaré Series by James W. Cogdell,Iiya Piatetski-Shapiro Pdf

The Arithmetic and Spectral Analysis of Poincaré series deals with the spectral properties of Poincaré series and their relation to Kloosterman sums. In addition to Poincaré series for an arbitrary Fuchsian group of the first kind, the spectral expansion of the Kloosterman-Selberg zeta function is analyzed, along with the adellic theory of Poincaré series and Kloosterman sums over a global function field. This volume is divided into two parts and begins with a discussion on Poincaré series and Kloosterman sums for Fuchsian groups of the first kind. A conceptual proof of Kuznetsov's formula and its generalization are presented in terms of the spectral analysis of Poincaré series in the framework of representation theory. An analysis of the spectral expansion of the Kloosterman-Selberg zeta function is also included. The second part develops the adellic theory of Poincaré series and Kloosterman sums over a global function field. The main result here is to show that in this context the analogue of the Linnik conjecture can be derived from the Ramanujan conjecture over function fields. Whittaker models, Kirillov models, and Bessel functions are also considered, along with the Kloosterman-spectral formula, convergence, and continuation. This book will be a valuable resource for students of mathematics.

Author : Paul Garrett
Publisher : Cambridge University Press
Page : 407 pages
File Size : 54,9 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 : David Ginzburg,Erez Lapid,David Soudry
Publisher : American Mathematical Soc.
Page : 315 pages
File Size : 53,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847060

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Automorphic Forms and $L$-functions I by David Ginzburg,Erez Lapid,David Soudry Pdf

Includes articles that represent global aspects of automorphic forms. This book covers topics such as: the trace formula; functoriality; representations of reductive groups over local fields; the relative trace formula and periods of automorphic forms; Rankin - Selberg convolutions and L-functions; and, p-adic L-functions.

Author : Shiing-Shen Chern,Friedrich Hirzebruch
Publisher : World Scientific
Page : 944 pages
File Size : 55,9 Mb
Release : 2000
Category : Mathematics
ISBN : 9812811761

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Wolf Prize in Mathematics by Shiing-Shen Chern,Friedrich Hirzebruch Pdf

Author : T. N. Bailey
Publisher : American Mathematical Soc.
Page : 490 pages
File Size : 53,9 Mb
Release : 1997
Category : Automorphic forms
ISBN : 9780821806098

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Representation Theory and Automorphic Forms by T. N. Bailey Pdf

The lectures from a course in the representation theory of semi- simple groups, automorphic forms, and the relations between them. The purpose is to help analysts make systematic use of Lie groups in work on harmonic analysis, differential equations, and mathematical physics; and to provide number theorists with the representation-theoretic input to Wiles's proof of Fermat's Last Theorem. Begins with an introductory treatment of structure theory and ends with the current status of functionality. Annotation copyrighted by Book News, Inc., Portland, OR

Author : Henryk Iwaniec
Publisher : American Mathematical Society, Revista Matemática Iberoamericana (RMI), Madrid, Spain
Page : 220 pages
File Size : 53,7 Mb
Release : 2021-11-17
Category : Mathematics
ISBN : 9781470466220

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Spectral Methods of Automorphic Forms by Henryk Iwaniec Pdf

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.

Author : János Pintz,András Biró,Kálmán Györy,Gergely Harcos,Miklós Simonovits,József Szabados
Publisher : Walter de Gruyter
Page : 418 pages
File Size : 40,6 Mb
Release : 2013-12-12
Category : Mathematics
ISBN : 9783110282429

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Number Theory, Analysis, and Combinatorics by János Pintz,András Biró,Kálmán Györy,Gergely Harcos,Miklós Simonovits,József Szabados Pdf

Paul Turán, one of the greatest Hungarian mathematicians, was born 100 years ago, on August 18, 1910. To celebrate this occasion the Hungarian Academy of Sciences, the Alfréd Rényi Institute of Mathematics, the János Bolyai Mathematical Society and the Mathematical Institute of Eötvös Loránd University organized an international conference devoted to Paul Turán's main areas of interest: number theory, selected branches of analysis, and selected branches of combinatorics. The conference was held in Budapest, August 22-26, 2011. Some of the invited lectures reviewed different aspects of Paul Turán's work and influence. Most of the lectures allowed participants to report about their own work in the above mentioned areas of mathematics.

Author : Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro
Publisher : American Mathematical Soc.
Page : 860 pages
File Size : 54,6 Mb
Release : 2000
Category : Mathematics
ISBN : 082180930X

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Selected Works of Ilya Piatetski-Shapiro by Ilʹi︠a︡ Iosifovich Pi︠a︡tet︠s︡kiĭ-Shapiro Pdf

This selection of papers of Ilya Piatetski-Shapiro represents almost 50 years of his mathematical activity. Included are many of his major papers in harmonic analysis, number theory, discrete groups, bounded homogeneous domains, algebraic geometry, automorphic forms, and automorphic L-functions. The papers in the volume are intended as a representative and accurate reflection of both the breadth and depth of Piatetski-Shapiro's work in mathematics. Some of his early works, such as those on the prime number theorem and on sets of uniqueness for trigonometric series, appear for the first time in English. Also included are several commentaries by his close colleagues. This volume offers an elegant representation of the contributions made by this renowned mathematician.

Author : Bretton Woods Workshop on Multiple Dirichlet Series
Publisher : American Mathematical Soc.
Page : 320 pages
File Size : 51,8 Mb
Release : 2006
Category : Dirichlet series
ISBN : 9780821839638

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Multiple Dirichlet Series, Automorphic Forms, and Analytic Number Theory by Bretton Woods Workshop on Multiple Dirichlet Series Pdf

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

Author : Zhi Qi
Publisher : American Mathematical Society
Page : 123 pages
File Size : 48,6 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781470443252

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Theory of Fundamental Bessel Functions of High Rank by Zhi Qi Pdf

In this article, the author studies fundamental Bessel functions for $mathrm{GL}_n(mathbb F)$ arising from the Voronoí summation formula for any rank $n$ and field $mathbb F = mathbb R$ or $mathbb C$, with focus on developing their analytic and asymptotic theory. The main implements and subjects of this study of fundamental Bessel functions are their formal integral representations and Bessel differential equations. The author proves the asymptotic formulae for fundamental Bessel functions and explicit connection formulae for the Bessel differential equations.

Author : Fernando Chamizo,Jordi Guàrdia, Antonio Rojas-León,José María Tornero
Publisher : American Mathematical Soc.
Page : 244 pages
File Size : 49,9 Mb
Release : 2015-09-28
Category : Number theory
ISBN : 9780821898581

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Trends in Number Theory by Fernando Chamizo,Jordi Guàrdia, Antonio Rojas-León,José María Tornero Pdf

This volume contains the proceedings of the Fifth Spanish Meeting on Number Theory, held from July 8-12, 2013, at the Universidad de Sevilla, Sevilla, Spain. The articles contained in this book give a panoramic vision of the current research in number theory, both in Spain and abroad. Some of the topics covered in this volume are classical algebraic number theory, arithmetic geometry, and analytic number theory. This book is published in cooperation with Real Sociedad Matemática Española (RSME).

Author : Gestur Olafsson,Joachim Hilgert
Publisher : Academic Press
Page : 303 pages
File Size : 45,5 Mb
Release : 1996-09-11
Category : Mathematics
ISBN : 9780080528724

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Causal Symmetric Spaces by Gestur Olafsson,Joachim Hilgert Pdf

This book is intended to introduce researchers and graduate students to the concepts of causal symmetric spaces. To date, results of recent studies considered standard by specialists have not been widely published. This book seeks to bring this information to students and researchers in geometry and analysis on causal symmetric spaces. Includes the newest results in harmonic analysis including Spherical functions on ordered symmetric space and the holmorphic discrete series and Hardy spaces on compactly casual symmetric spaces Deals with the infinitesimal situation, coverings of symmetric spaces, classification of causal symmetric pairs and invariant cone fields Presents basic geometric properties of semi-simple symmetric spaces Includes appendices on Lie algebras and Lie groups, Bounded symmetric domains (Cayley transforms), Antiholomorphic Involutions on Bounded Domains and Para-Hermitian Symmetric Spaces

Author : Lin Weng,Masanobu Kaneko
Publisher : World Scientific
Page : 383 pages
File Size : 48,9 Mb
Release : 2007
Category : Science
ISBN : 9789812705044

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The Conference on L-Functions by Lin Weng,Masanobu Kaneko Pdf

This invaluable volume collects papers written by many of the world's top experts on L-functions. It not only covers a wide range of topics from algebraic and analytic number theories, automorphic forms, to geometry and mathematical physics, but also treats the theory as a whole. The contributions reflect the latest, most advanced and most important aspects of L-functions. In particular, it contains Hida's lecture notes at the conference and at the Eigenvariety semester in Harvard University and Weng's detailed account of his works on high rank zeta functions and non-abelian L-functions.

Author : James Cogdell,Simon Gindikin,Peter Sarnak
Publisher : American Mathematical Society
Page : 852 pages
File Size : 46,9 Mb
Release : 2022-11-03
Category : Mathematics
ISBN : 9781470454944

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Selected Works of Ilya Piatetski-Shapiro by James Cogdell,Simon Gindikin,Peter Sarnak Pdf

This selection of papers of I. Piatetski-Shapiro represents almost 50 years of his mathematical activity. Included are many of his major papers in harmonic analysis, number theory, discrete groups, bounded homogeneous domains, algebraic geometry, automorphic forms, and automorphic $L$-functions. The papers in the volume are intended as a representative and accurate reflection of both the breadth and depth of Piatetski-Shapiro's work in mathematics. Some of his early works, such as those on the prime number theorem and on sets of uniqueness for trigonometric series, appear for the first time in English. Also included are several commentaries by his close colleagues. This volume offers an elegant representation of the contributions made by this renowned mathematician.

Author : Anonim
Publisher : Elsevier
Page : 343 pages
File Size : 50,7 Mb
Release : 1996-09-27
Category : Mathematics
ISBN : 9780080526959

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Algebraic and Analytic Methods in Representation Theory by Anonim Pdf

This book is a compilation of several works from well-recognized figures in the field of Representation Theory. The presentation of the topic is unique in offering several different points of view, which should makethe book very useful to students and experts alike. Presents several different points of view on key topics in representation theory, from internationally known experts in the field