Alternate proof of Shô Iseki's functional equation
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.
scientific article; zbMATH DE number 1371466