A fresh approach to classical Eisenstein series and the newer Hilbert–Eisenstein series

Author:

Butzer Paul L.1,Pogány Tibor K.23

Affiliation:

1. Lehrstuhl A für Mathematik, RWTH Aachen, D–52056 Aachen, Germany

2. John von Neumann Faculty of Informatics, Óbuda University, 1034–Budapest, Hungary

3. Faculty of Maritime Studies, University of Rijeka, HR–51000 Rijeka, Croatia

Abstract

This paper is concerned with new results for the circular Eisenstein series [Formula: see text] as well as with a novel approach to Hilbert–Eisenstein series [Formula: see text], introduced by Michael Hauss in 1995. The latter turns out to be the product of the hyperbolic sinh function with an explicit closed form linear combination of digamma functions. The results, which include differentiability properties and integral representations, are established by independent and different argumentations. Highlights are new results on the Butzer–Flocke–Hauss Omega function, one basis for the study of Hilbert–Eisenstein series, which have been the subject of several recent papers.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

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