Automorphic pairs of distributions on ℝ, and Maass forms of real weights

2020/02/26 by Miyazaki, Tadashi
#11F12 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2002.11285

Abstract

We give a correspondence between automorphic pairs of distributions on ℝ and Dirichlet series satisfying functional equations and some additional analytic conditions. Moreover, we show that the notion of automorphic pairs of distributions on ℝ can be regarded as a generalization of automorphic distributions on smooth principal series representations of the universal covering group of SL(2,ℝ). As an application, we prove Weil type converse theorems for automorphic distributions and Maass forms of real weights.

Related

• Converse theorems for automorphic distributions and Maass forms of level N
• Pairings of automorphic distributions
• Adelization of Automorphic Distributions and Mirabolic Eisenstein Series
• Independent linear forms on the group Ω_p
• The Ramanujan-Petersson and Selberg conjectures for Maass forms