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Author: Olga Balkanova Publisher: ISBN: Category : Languages : en Pages : 128
Book Description
The main result of this dissertation is an asymptotic formula for the fourth moment of automorphic L-functions of prime power level [rho vu], [vu] --> [infinity]. This is a continuation of the work of Rouymi, who computed the first three moments at prime power level, and a generalisation of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam.
Author: Olga Balkanova Publisher: ISBN: Category : Languages : en Pages : 128
Book Description
The main result of this dissertation is an asymptotic formula for the fourth moment of automorphic L-functions of prime power level [rho vu], [vu] --> [infinity]. This is a continuation of the work of Rouymi, who computed the first three moments at prime power level, and a generalisation of results obtained for prime level by Duke, Friedlander & Iwaniec and Kowalski, Michel & Vanderkam.
Author: Dihua Jiang Publisher: American Mathematical Soc. ISBN: 147041709X Category : Mathematics Languages : en Pages : 386
Book Description
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.
Author: Alexander Lu Beckwith Publisher: ISBN: Category : Automorphic functions Languages : en Pages : 173
Book Description
We study the behavior of families of L-functions at exhibiting conductor-dropping behavior. We will derive asymptotic expansions of the short interval first and second moments of GL(2)xGL(2) L-functions at special points with power-saving error terms. As a consequence, we show that large number of cusp forms for Hecke congruence surfaces of prime level are simultaneously destroyed in two directions of the associated Teichmuller space. We also establish upper bounds for the second moment of GL(2)xGL(3) L-functions and the sixth moment of GL(2) L-functions at special points as the spectral parameter varies in a short interval.
Author: Henryk Iwaniec Publisher: American Mathematical Soc. ISBN: 0821807773 Category : Mathematics Languages : en Pages : 274
Book Description
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
Author: Philipp Fleig Publisher: Cambridge Studies in Advanced ISBN: 1107189926 Category : Mathematics Languages : en Pages : 587
Book Description
Detailed exposition of automorphic representations and their relation to string theory, for mathematicians and theoretical physicists.
Author: Nicholas M. Katz Publisher: Princeton University Press ISBN: 9780691084336 Category : Mathematics Languages : en Pages : 262
Book Description
The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.
Author: Henryk Iwaniec Publisher: American Mathematical Soc. ISBN: 1470467704 Category : Education Languages : en Pages : 615
Book Description
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: Olga Balkanova
Author: Olga Balkanova
Author: E. Kowalski
Author: Dihua Jiang
Author: Alexander Lu Beckwith
Author: Henryk Iwaniec
Author: 
Author: Philipp Fleig
Author: Nicholas M. Katz
Author: H. Jacquet
Author: Henryk Iwaniec