Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Generalized Eta Transformation Formulas as the Hecke Modular Relation

Version 1 : Received: 14 March 2024 / Approved: 16 March 2024 / Online: 18 March 2024 (08:12:55 CET)

A peer-reviewed article of this Preprint also exists.

Wang, N.; Kuzumaki, T.; Kanemitsu, S. The Generalized Eta Transformation Formulas as the Hecke Modular Relation. Axioms 2024, 13, 304. Wang, N.; Kuzumaki, T.; Kanemitsu, S. The Generalized Eta Transformation Formulas as the Hecke Modular Relation. Axioms 2024, 13, 304.

Abstract

Transformation formula under the action of a general linear fractional transformation for generalized Dedekind eta-function has been a subject of intensive study, Rademacher, Dieter, Meyer et al. However, the (Hecke) modular relation structure has not been recognized until the work of Goldstein-de la Torre, and streamlining the classical proofs in the modular relation will reveal the meaning hidden in those works. Our main aim is to elucidate the works of these researchers in the context of modular relations.

Keywords

RHB correspondence; transformation formula for Lambert series; Hurwitz zeta-function; Lerch zeta-function; vector space structure

Subject

Computer Science and Mathematics, Algebra and Number Theory

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