The Generalized Eta Transformation Formulas as the Hecke Modular Relation

Nianliang Wang; Takato kuzumaki; Shigeru Kanemitsu

doi:10.20944/preprints202403.0963.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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.

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

Computer Science and Mathematics, Algebra and Number Theory

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The Generalized Eta Transformation Formulas as the Hecke Modular Relation

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