On Unfoldings of Some Integrals of Automorphic Functions on General Linear Groups
Eleftherios Tsiokos

TL;DR
This paper investigates certain integrals of automorphic functions on general linear groups, utilizing Fourier coefficients to gain new insights into their structure and properties.
Contribution
It introduces new methods for analyzing integrals of automorphic functions using Fourier coefficients, extending previous results and providing deeper understanding of their unfoldings.
Findings
Derived new formulas for integrals involving Fourier coefficients
Extended Fourier coefficient analysis to broader classes of automorphic forms
Provided new insights into the structure of automorphic integrals on GL(n)
Abstract
We use results about Fourier coefficients appearing in [T] (and some more obtained here), to obtain information for certain among the integrals of the form where: is the adele ring of a number field ; is a -cuspidal automorphic form; is a -automorphic function (even the trivial for some results); is a -automorphic form for a multiple of ; is a Fourier coefficient of for certain choices of additive functions in a set which we defined in is a diagonal embedding of in ; of course ; and is the center of .
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Taxonomy
Topicsadvanced mathematical theories · Advanced Differential Equations and Dynamical Systems · Algebraic and Geometric Analysis
