Number theory, trace formulas, and discrete groups : symposium in honor of Atle Selberg, Oslo, Norway, July 14-21, 1987

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. Content: Inside Front Cover, Page ii Front Matter, Page iii Copyright, Page iv Contributors, Pages ix-xi Participants in the Selberg Symposium, 1987, Pages xiii-xiv Inside Front Cover, Page xv Preface, Pages xvii-xviii, Karl Egil Aubert Foreword, Pages xix-xx, Enrico Bombieri 1 - Prehistory of the Zeta-Function, Pages 1-9, ANDRÉ WEIL 2 - The Trace Formula and Hecke Operators, Pages 11-27, JAMES ARTHUR 3 - Selberg's Sieve and Its Applications, Pages 29-48, ENRICO BOMBIERI 4 - The Rankin–Selberg Method: A Survey, Pages 49-109, DANIEL BUMP 5 - On the Base Change Problem:, Pages 111-124, After J. Arthur, L. Clozel 6 - Eisenstein Series, the Trace Formula, and the Modern Theory of Automorphic Forms, Pages 125-155, R.P. LANGLANDS 7 - Selberg's Work on the Zeta-Function, Pages 157-168, HUGH L. MONTGOMERY 8 - Selberg's Work on the Arithmeticity of Lattices and its Ramifications, Pages 169-183, G.D. MOSTOW 9 - Mean Values of the Riemann Zeta-Function with Application to the Distribution of Zeros, Pages 185-199, J.B. CONREY, A. GHOSH, S.M. GONEK 10 - Geometric Ramanujan Conjecture and Drinfeld Reciprocity Law, Pages 201-218, YUVAL Z. FLICKER, DAVID A. KAZHDAN 11 - On the Brun-Titchmarsh Theorem, Pages 219-228, JOHN B. FRIEDLANDER 12 - A Double Sum Over Primes and Zeros of the Zeta-Function, Pages 229-240, P.X. GALLAGHER 13 - Integral Representations of Eisenstein series and L-functions, Pages 241-264, PAUL B. GARRETT 14 - Recent Results on Automorphic L-Functions, Pages 265-280, S. GELBART 15 - Explicit Formulae as Trace Formulae, Pages 281-288, DORIAN GOLDFELD 16 - Some Remarks on the Sieve Method, Pages 289-308, GEORGE GREAVES 17 - Critical Zeros of GL(2) L-Functions, Pages 309-330, JAMES LEE HAFNER 18 - A New Upper Bound in the Linear Sieve, Pages 331-341, H. HALBERSTAM, LOU SHITUO, YAO QI 19 - On the Distribution of log∣ζ′(1/2+ it)∣, Pages 343-370, DENNIS A. HEJHAL 20 - Selberg's Lower Bound of the First Eigenvalue for Congruence Groups, Pages 371-375, H. IWANIEC 21 - Discrete Subgroups and Ergodic Theory, Pages 377-398, G.A. MARGULIS 22 - Good Rational Approximation Derived from Thue's Inequality, Pages 399-408, JULIA MUELLER 23 - The Selberg Zeta-Function of a Kleinian Group, Pages 409-441, S.J. PATTERSON 24 - Nonarithmetic Lattices in Lobachevsky Spaces of Arbitrary Dimension, Pages 443-444, J. PIATETSKI-SHAPIRO 25 - On Some Functions Connected with the Sieve, Pages 445-455, H.-E. RICHERT 26 - Special Values of Selberg's Zeta-function, Pages 457-465, P. SARNAK 27 - Sifting Problems, Sifting Density, and Sieves, Pages 467-484, ATLE SELBERG 28 - Remarks on the Sieving Limit of the Buchstab-Rosser Sieve, Pages 485-502, KAI-MAN TSANG 29 - Recent Work on Waring's Problem, Pages 503-510, R.C. VAUGHAN