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.
Citation
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
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