The Critical Values Of Exterior Square L Functions On Gl2
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Automorphic Representations, L-Functions and Applications: Progress and Prospects
Author | : James W. Cogdell |
Publisher | : Walter de Gruyter |
Total Pages | : 441 |
Release | : 2011-06-24 |
Genre | : Mathematics |
ISBN | : 3110892707 |
This volume is the proceedings of the conference on Automorphic Representations, L-functions and Applications: Progress and Prospects, held at the Department of Mathematics of The Ohio State University, March 27–30, 2003, in honor of the 60th birthday of Steve Rallis. The theory of automorphic representations, automorphic L-functions and their applications to arithmetic continues to be an area of vigorous and fruitful research. The contributed papers in this volume represent many of the most recent developments and directions, including Rankin–Selberg L-functions (Bump, Ginzburg–Jiang–Rallis, Lapid–Rallis) the relative trace formula (Jacquet, Mao–Rallis) automorphic representations (Gan–Gurevich, Ginzburg–Rallis–Soudry) representation theory of p-adic groups (Baruch, Kudla–Rallis, Mœglin, Cogdell–Piatetski-Shapiro–Shahidi) p-adic methods (Harris–Li–Skinner, Vigneras), and arithmetic applications (Chinta–Friedberg–Hoffstein). The survey articles by Bump, on the Rankin–Selberg method, and by Jacquet, on the relative trace formula, should be particularly useful as an introduction to the key ideas about these important topics. This volume should be of interest both to researchers and students in the area of automorphic representations, as well as to mathematicians in other areas interested in having an overview of current developments in this important field.
Degree 16 Standard L-function of $GSp(2) \times GSp(2)$
Author | : Dihua Jiang |
Publisher | : American Mathematical Soc. |
Total Pages | : 210 |
Release | : 1996 |
Genre | : Mathematics |
ISBN | : 0821804766 |
Automorphic L-functions, introduced by Robert Langlands in the 1960s, are natural extensions of such classical L-functions as the Riemann zeta function, Hecke L-functions, etc. They form an important part of the Langlands Program, which seeks to establish connections among number theory, representation theory, and geometry. This book offers, via the Rankin-Selberg method, a thorough and comprehensive examination of the degree 16 standard L-function of the product of two rank two symplectic similitude groups, which includes the study of the global integral of Rankin-Selberg type and local integrals, analytic properties of certain Eisenstein series of symplectic groups, and the relevant residue representations.
The Behaviour of L-functions at the Edge of the Critical Strip and Applications
Author | : Xiannan Li |
Publisher | : Stanford University |
Total Pages | : 99 |
Release | : 2011 |
Genre | : |
ISBN | : |
A large number of problems in number theory can be reduced to statements about L-functions. In this thesis, we study L-functions at the edge of the critical strip, and relate these to a variety of objects of arithmetic interest.
P-adic Aspects Of Modular Forms
Author | : Baskar Balasubramanyam |
Publisher | : World Scientific |
Total Pages | : 342 |
Release | : 2016-06-14 |
Genre | : Mathematics |
ISBN | : 9814719242 |
The aim of this book is to give a systematic exposition of results in some important cases where p-adic families and p-adic L-functions are studied. We first look at p-adic families in the following cases: general linear groups, symplectic groups and definite unitary groups. We also look at applications of this theory to modularity lifting problems. We finally consider p-adic L-functions for GL(2), the p-adic adjoint L-functions and some cases of higher GL(n).
Algorithmic Number Theory
Author | : Florian Hess |
Publisher | : Springer |
Total Pages | : 609 |
Release | : 2006-10-05 |
Genre | : Mathematics |
ISBN | : 354036076X |
This book constitutes the refereed proceedings of the 7th International Algorithmic Number Theory Symposium, ANTS 2006, held in Berlin, July 2006. The book presents 37 revised full papers together with 4 invited papers selected for inclusion. The papers are organized in topical sections on algebraic number theory, analytic and elementary number theory, lattices, curves and varieties over fields of characteristic zero, curves over finite fields and applications, and discrete logarithms.
On Central Critical Values of the Degree Four $L$-functions for $\mathrm {GSp}(4)$: The Fundamental Lemma
Author | : Masaaki Furusawa |
Publisher | : American Mathematical Soc. |
Total Pages | : 158 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821833286 |
Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].
Proceedings of the International Conference on Cohomology of Arithmetic Groups, L-Functions, and Automorphic Forms
Author | : T. N. Venkataramana |
Publisher | : Alpha Science International, Limited |
Total Pages | : 270 |
Release | : 2001 |
Genre | : Mathematics |
ISBN | : |
This collection of papers is based on lectures delivered at the Tata Institute of Fundamental Research (TIFR) as part of a special year on arithmetic groups, $L$-functions and automorphic forms. The volume opens with an article by Cogdell and Piatetski-Shapiro on Converse Theorems for $GL_n$ and applications to liftings. It ends with some remarks on the Riemann Hypothesis by Ram Murty. Other talks cover topics such as Hecke theory for Jacobi forms, restriction maps and $L$-values, congruences for Hilbert modular forms, Whittaker models for $p$-adic $GL(4)$, the Seigel formula, newforms for the Maass Spezialchar, an algebraic Chebotarev density theorem, a converse theorem for Dirichlet series with poles, Kirillov theory for $GL_2(\mathcal{D})$, and the $L^2$ Euler characteristic of arithmetic quotients. The present volume is the latest in the Tata Institute's tradition of recognized contributions to number theory.
The Second Moment Theory of Families of $L$-Functions–The Case of Twisted Hecke $L$-Functions
Author | : Valentin Blomer |
Publisher | : American Mathematical Society |
Total Pages | : 160 |
Release | : 2023-02-13 |
Genre | : Mathematics |
ISBN | : 1470456788 |
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