On Central Critical Values Of The Degree Four L Functions For Mathrm Gsp4 The Fundamental Lemma
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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}].
Author | : Masaaki Furusawa |
Publisher | : |
Total Pages | : 134 |
Release | : 2014-09-11 |
Genre | : Automorphic forms |
ISBN | : 9781470410575 |
Some time ago, the first and third authors proposed two relative trace formulas to prove generalizations of B{uml}ocherer's conjecture on the central critical values of the degree four L-functions for GSp(4), and proved the relevant fundamental lemmas. Recently, the first and second authors proposed an alternative third relative trace formula to approach the same problem and proved the relevant fundamental lemma. In this paper the authors extend the latter fundamental lemma and the first of the former fundamental lemmas to the full Hecke algebra. The fundamental lemma is an equality of two local relative orbital integrals. In order to show that they are equal, the authors compute them explicitly for certain bases of the Hecke algebra and deduce the matching.
Author | : Masaaki Furusawa |
Publisher | : |
Total Pages | : 139 |
Release | : 2014-09-11 |
Genre | : Automorphic forms |
ISBN | : 9781470403805 |
Statement of results Gauss sum, Kloosterman sum and Salie sum Matrix argument Kloosterman sums Evaluation of the Novodvorsky orbital integral Evaluation of the Bessel orbital integral Evaluation of the quadratic orbital integral Bibliography.
Author | : M. Ram Murty |
Publisher | : Springer Science & Business Media |
Total Pages | : 205 |
Release | : 2012-01-05 |
Genre | : Mathematics |
ISBN | : 3034802730 |
This volume develops methods for proving the non-vanishing of certain L-functions at points in the critical strip. It begins at a very basic level and continues to develop, providing readers with a theoretical foundation that allows them to understand the latest discoveries in the field.
Author | : Jr̲n Steuding |
Publisher | : Springer Science & Business Media |
Total Pages | : 320 |
Release | : 2007-06-06 |
Genre | : Mathematics |
ISBN | : 3540265260 |
These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.
Author | : Yasuko Hasegawa |
Publisher | : |
Total Pages | : 18 |
Release | : 2013 |
Genre | : |
ISBN | : |
Author | : Mathematical Sciences Research Institute (Berkeley, Calif.). |
Publisher | : |
Total Pages | : 26 |
Release | : 1987 |
Genre | : |
ISBN | : |
Author | : Gaëtan Chenevier |
Publisher | : Springer |
Total Pages | : 428 |
Release | : 2019-02-28 |
Genre | : Mathematics |
ISBN | : 3319958917 |
This book includes a self-contained approach of the general theory of quadratic forms and integral Euclidean lattices, as well as a presentation of the theory of automorphic forms and Langlands' conjectures, ranging from the first definitions to the recent and deep classification results due to James Arthur. Its connecting thread is a question about lattices of rank 24: the problem of p-neighborhoods between Niemeier lattices. This question, whose expression is quite elementary, is in fact very natural from the automorphic point of view, and turns out to be surprisingly intriguing. We explain how the new advances in the Langlands program mentioned above pave the way for a solution. This study proves to be very rich, leading us to classical themes such as theta series, Siegel modular forms, the triality principle, L-functions and congruences between Galois representations. This monograph is intended for any mathematician with an interest in Euclidean lattices, automorphic forms or number theory. A large part of it is meant to be accessible to non-specialists.
Author | : Helmut Klingen |
Publisher | : Cambridge University Press |
Total Pages | : 0 |
Release | : 1990-02-23 |
Genre | : Mathematics |
ISBN | : 0521350522 |
From their inception, Siegel modular forms have been studied extensively because of their significance in both automorphic functions in several complex variables and number theory. The comprehensive theory of automorphic forms to subgroups of algebraic groups and the arithmetical theory of modular forms illustrate these two aspects in an illuminating manner. The author's aim is to present a straightforward and easily accessible survey of the main ideas of the theory at an elementary level, providing a sound basis from which the reader can study advanced works and undertake original research. This book is based on lectures given by the author for a number of years and is intended for a one-semester graduate course, though it can also be used profitably for self-study. The only prerequisites are a basic knowledge of algebra, number theory and complex analysis.
Author | : Werner Müller |
Publisher | : |
Total Pages | : 0 |
Release | : 2021 |
Genre | : |
ISBN | : 9783030685072 |
A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur's trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.