منابع مشابه
Automorphic Representations and Number Theory *
An excellent introduction to the theory of automorphic representations and the relations with number theory is the Corvallis proceedings, Automorphic Forms, Representations and L-Functions, Parts 1 and 2, Proc. Sympos. Pure Math., vol. 33, 1979. Although composed mainly of survey articles, the proceedings are already rather formidable. They are a measure of the breadth of the field. They will b...
متن کاملOn Some Applications of Automorphic Forms to Number Theory
A basic idea of Dirichlet is to study a collection of interesting quantities {an}n≥1 by means of its Dirichlet series in a complex variable w: ∑ n≥1 ann −w. In this paper we examine this construction when the quantities an are themselves infinite series in a second complex variable s, arising from number theory or representation theory. We survey a body of recent work on such series and present...
متن کاملScattering Theory for Automorphic Functions
This paper is an expository account of our 1976 monograph [6] on Scattering theory for automorphic functions. Several improvements have been incorporated: a more direct proof of the meromorphic character of the Eisenstein series, an explicit formula for the translation representations and a simpler derivation of the spectral representations. Our hyperbolic approach to the Selberg trace formula ...
متن کاملModern Theory of Automorphic Forms ∗
The modern theory of automorphic forms is a response to many different impulses and influences, above all the work of Hecke, but also class-field theory and the study of quadratic forms, the theory of representations of reductive groups, and of complexmultiplication, but so far many of the most powerful techniques are the issue, direct or indirect, of the introduction by Maass and then Selberg ...
متن کاملM-theory and automorphic scattering
The strongly coupled limit of string scattering and the automorphic construction of the graviton S-matrix is compared with the eleven dimensional formulation of Mtheory. In a particular scaling limit at strong string coupling, M-theory is described by eleven-dimensional supergravity which does not possess a dilaton, but rather a perturbative expansion in the gravitational coupling and derivativ...
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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 2003
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.2003.v2003.n1.a2