A Note on a Fourier Expansion of Automorphic Functions that Nontrivially Involves the Euclidean Algorithm
Eleftherios Tsiokos
TL;DR
This paper extends the Fourier expansion of automorphic functions to include the Euclidean algorithm nontrivially and explores its potential application in the Rankin-Selberg method.
Contribution
It introduces a novel Fourier expansion incorporating the Euclidean algorithm and discusses its application in automorphic forms analysis.
Findings
Extended Fourier expansion with Euclidean algorithm
Potential application in Rankin-Selberg method
New perspective on automorphic functions
Abstract
We extend the Fourier expansion of automorphic functions of Piateski-Shapiro and Shalika in a way that the Euclidean algorithm appears nontrivially. Then, we discuss a potential application in the Rankin-Selberg method.
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Taxonomy
TopicsStochastic processes and financial applications · Mathematical functions and polynomials · Advanced Mathematical Modeling in Engineering