Automorphic integrals with log-polynomial period functions and arithmetical identities

Tewlede G/Egziabher, Hunduma Legesse Geleta, Abdul Hassen

Research output: Contribution to journalArticlepeer-review

Abstract

Building on the works of S. Bochner on equivalence of modular relation with functional equation associated to the Dirichlet series, K. Chandrasekharan and R. Narasimhan obtained new equivalences between the functional equation and some arithmetical identities. Sister Ann M. Heath considered the functional equation in the Hawkins and Knopp context and showed its equivalence to two arithmetical identities associated with entire modular cusp integrals involving rational period functions for the full modular group. In this paper we use techniques of Chandrasekharan and Narasimhan to prove results analogous to those of Sister Ann M. Heath. Specifically, we establish equivalence of two arithmetical identities with a functional equation associated with automorphic integrals involving log-polynomial-period functions on the discrete Hecke groups.

Original languageEnglish (US)
Pages (from-to)854-870
Number of pages17
JournalIndagationes Mathematicae
Volume34
Issue number4
DOIs
StatePublished - Jul 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics

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