Dirichlet Series With Functional Equations, Automorphic Integrals and Arithmetical Identities
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Date
2020-07-14
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Addis Ababa University
Abstract
Chanrasekharan and Narasimhan in [2] have shown that the functional equation Γ(s)ϕ(s) = Γ(δ−s)ψ(δ−s) is equivalent to two arithmetical identities. In
[5] Hawkins and Knopp proved a Hecke correspondence theorem for modular
integrals with rational period function on Γθ, a sub group of the full modular
group Γ(1).
Sister Ann M. Heath in [1] considered the functional equation in the Hawkins
and Knopp context. Analogous to Chandrasekharan and Narasimhan she
showed its equivalence to two arithmetical identities associated with entire
modular cusp integrals involving rational period functions for the full modular
group.
In this dissertation we extend the results of Sister Ann M. Heath to entire
automorphic integrals involving rational period functions on discrete Hecke
group G(λ), λ > 0. Moreover, we establish equivalence of two arithmetical
identities with a functional equation associated with automorphic integrals
involving log-polynomial-period functions on the Hecke groups.
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Dirichlet Series With Functional Equations, Automorphic Integrals, Arithmetical Identities