Alternate proof of Shô Iseki's functional equation
type: Item
instance of: scholarly article
title: Alternate proof of Shô Iseki's functional equation
zbMATH Open document ID: 0959.11018
DOI: 10.1023/A:1009831420415
author: Ankur Basu
published in: The Ramanujan Journal
publication date: 1999-11-29T00:00:00Z
review text: A functional equation derived by \textit{S. Iseki} [Duke Math. J. 24, 653-662 (1957; Zbl 0093.25903)] includes as special cases the transformation theory of the Dedekind modular function \(\eta(\tau)\) and of the reviewer's Lambert series \(G_p(e^{2\pi i\tau})\). Heretofore, the proofs of Iseki's formula relied on complex integration and residue calculus. This paper gives a shorter and simpler proof using Fourier series.
Mathematics Subject Classification ID: 11F20
zbMATH DE Number: 1371466
zbMATH Keywords: functional equation
zbMATH Keywords: Dedekind modular function
zbMATH Keywords: Lambert series
reviewed by: Tom M. Apostol
MaRDI profile type: Publication
full work available at URL: a:1009831420415
OpenAlex ID: W138340538
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description: scientific article; zbMATH DE number 1371466