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September 2022 Automorphic pairs of distributions on $\mathbb{R}$ and Maass forms of real weight
Tadashi Miyazaki
Funct. Approx. Comment. Math. 67(1): 77-143 (September 2022). DOI: 10.7169/facm/1990

Abstract

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

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Tadashi Miyazaki. "Automorphic pairs of distributions on $\mathbb{R}$ and Maass forms of real weight." Funct. Approx. Comment. Math. 67 (1) 77 - 143, September 2022. https://doi.org/10.7169/facm/1990

Information

Published: September 2022
First available in Project Euclid: 17 March 2022

Digital Object Identifier: 10.7169/facm/1990

Subjects:
Primary: 11F12
Secondary: 11F70

Keywords: automorphic distributions , converse theorem , Dirichlet series , Maass forms

Rights: Copyright © 2022 Adam Mickiewicz University

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Vol.67 • No. 1 • September 2022
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