Author : Masaaki Furusawa
Publisher : American Mathematical Soc.
Page : 158 pages
File Size : 20,9 MB
Release : 2003
Category : 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 :
Page : 134 pages
File Size : 37,52 MB
Release : 2014-09-11
Category : 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 :
Page : 139 pages
File Size : 35,74 MB
Release : 2014-09-11
Category : 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 : Gaëtan Chenevier
Publisher : Springer
Page : 428 pages
File Size : 26,10 MB
Release : 2019-02-28
Category : 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 : Ameya Pitale
Publisher : Springer
Page : 142 pages
File Size : 22,81 MB
Release : 2019-05-07
Category : Mathematics
ISBN : 3030156753
This monograph introduces two approaches to studying Siegel modular forms: the classical approach as holomorphic functions on the Siegel upper half space, and the approach via representation theory on the symplectic group. By illustrating the interconnections shared by the two, this book fills an important gap in the existing literature on modular forms. It begins by establishing the basics of the classical theory of Siegel modular forms, and then details more advanced topics. After this, much of the basic local representation theory is presented. Exercises are featured heavily throughout the volume, the solutions of which are helpfully provided in an appendix. Other topics considered include Hecke theory, Fourier coefficients, cuspidal automorphic representations, Bessel models, and integral representation. Graduate students and young researchers will find this volume particularly useful. It will also appeal to researchers in the area as a reference volume. Some knowledge of GL(2) theory is recommended, but there are a number of appendices included if the reader is not already familiar.
Author : Baskar Balasubramanyam
Publisher : World Scientific
Page : 342 pages
File Size : 47,46 MB
Release : 2016-06-14
Category : 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).
Author : Helmut Klingen
Publisher : Cambridge University Press
Page : 0 pages
File Size : 42,50 MB
Release : 1990-02-23
Category : 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 :
Page : 0 pages
File Size : 26,35 MB
Release : 2021
Category :
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.
Author : Scott Harper
Publisher : Springer Nature
Page : 154 pages
File Size : 20,82 MB
Release : 2021-05-25
Category : Mathematics
ISBN : 3030741001
This monograph studies generating sets of almost simple classical groups, by bounding the spread of these groups. Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group, every nontrivial element belongs to a generating pair. Groups with this property are said to be 3/2-generated. Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient is cyclic. We prove a strong version of this conjecture for almost simple classical groups, by bounding the spread of these groups. This involves analysing the automorphisms, fixed point ratios and subgroup structure of almost simple classical groups, so the first half of this monograph is dedicated to these general topics. In particular, we give a general exposition of Shintani descent. This monograph will interest researchers in group generation, but the opening chapters also serve as a general introduction to the almost simple classical groups.
Author : Christian W. Fabjan
Publisher : Springer Nature
Page : 1083 pages
File Size : 44,88 MB
Release : 2020
Category : Elementary particles (Physics).
ISBN : 3030353184
This second open access volume of the handbook series deals with detectors, large experimental facilities and data handling, both for accelerator and non-accelerator based experiments. It also covers applications in medicine and life sciences. A joint CERN-Springer initiative, the "Particle Physics Reference Library" provides revised and updated contributions based on previously published material in the well-known Landolt-Boernstein series on particle physics, accelerators and detectors (volumes 21A, B1,B2,C), which took stock of the field approximately one decade ago. Central to this new initiative is publication under full open access
