Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg, Oslo, Norway, July 14–21, 1987Karl Egil Aubert, Enrico Bombieri, Dorian Goldfeld Academic Press, 10 de maig 2014 - 532 pàgines Number Theory, Trace Formulas and Discrete Groups: Symposium in Honor of Atle Selberg Oslo, Norway, July 14-21, 1987 is a collection of papers presented at the 1987 Selberg Symposium, held at the University of Oslo. This symposium contains 30 lectures that cover the significant contribution of Atle Selberg in the field of mathematics. This book is organized into three parts encompassing 29 chapters. The first part presents a brief introduction to the history and developments of the zeta-function. The second part contains lectures on Selberg's considerable research studies on understanding the principles of several aspects of mathematics, including in modular forms, the Riemann zeta function, analytic number theory, sieve methods, discrete groups, and trace formula. The third part is devoted to Selberg's further research works on these topics, with particular emphasis on their practical applications. Some of these research studies, including the integral representations of Einstein series and L-functions; first eigenvalue for congruence groups; the zeta function of a Kleinian group; and the Waring's problem are discussed. This book will prove useful to mathematicians, researchers, and students. |
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1989 by Academic Academic Press analytic continuation arithmetic assume asymptotic automorphic form automorphic L-functions automorphic representation character cocompact compact conjecture conjugacy classes consider constant convergent corresponding critical line cusp forms cuspidal defined denote Dirichlet series DISCRETE GROUPS ISBN eigenvalues Eisenstein series elements estimate Euler product example finite follows form reserved Fourier coefficients function f functional equation Gelbart GL(n Hecke holomorphic inequality invariant irreducible isomorphic Iwaniec Jacquet Kloosterman sums Langlands lattice Lemma linear sieve log log lower bound Ls(s Maass forms matrix meromorphic modular forms multiple nonzero notation Number Theory obtain orbital integrals parabolic subgroup Piatetski–Shapiro Poincaré series poles polynomial prime factors problem Proc proof proved Rankin-Selberg convolution Rankin-Selberg method Re(s result rights of reproduction satisfies Section Selberg Selberg trace formula semisimple Shalika sieve method space Suppose symmetric Theorem tion trace formula unipotent unramified upper bound Whittaker function zeros zeta function