On the structure of the Selberg class, VII: 1 < d < 2
成果类型：
Article
署名作者：
Kaczorowski, Jerzy; Perelli, Alberto
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
DOI：
10.4007/annals.2011.173.3.4
发表日期：
2011
页码：
1397-1441
关键词：
摘要：
The Selberg class S is a rather general class of Dirichlet series with functional equation and Euler product and can be regarded as an axiomatic model for the global L-functions arising from number theory and automorphic representations. One of the main problems of the Selberg class theory is to classify the elements of S. Such a classification is based on a real-valued invariant d called degree, and the degree conjecture asserts that d is an element of N for every L-functionin S. The degree conjecture has been proved for d < 5/3, and in this paper we extend its validity to d < 2. The proof requires several new ingredients, in particular a rather precise description of the properties of certain nonlinear twists associated with the L-functions in S.