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Keywords = ramified functional equation

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24 pages, 420 KB  
Article
Unified Theory of Zeta-Functions Allied to Epstein Zeta-Functions and Associated with Maass Forms
by Nianliang Wang, Takako Kuzumaki and Shigeru Kanemitsu
Mathematics 2023, 11(4), 917; https://doi.org/10.3390/math11040917 - 11 Feb 2023
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Abstract
In this paper, we shall establish a hierarchy of functional equations (as a G-function hierarchy) by unifying zeta-functions that satisfy the Hecke functional equation and those corresponding to Maass forms in the framework of the ramified functional equation with (essentially) two gamma [...] Read more.
In this paper, we shall establish a hierarchy of functional equations (as a G-function hierarchy) by unifying zeta-functions that satisfy the Hecke functional equation and those corresponding to Maass forms in the framework of the ramified functional equation with (essentially) two gamma factors through the Fourier–Whittaker expansion. This unifies the theory of Epstein zeta-functions and zeta-functions associated to Maass forms and in a sense gives a method of construction of Maass forms. In the long term, this is a remote consequence of generalizing to an arithmetic progression through perturbed Dirichlet series. Full article
(This article belongs to the Special Issue Analytic Methods in Number Theory and Allied Fields)
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