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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
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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