On an identity of Ramanujan over finitely generated domains

Gabriella Hajdu; Lajos Hajdu

doi:10.1007/s10474-006-0070-4

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Acta Mathematica Hungarica

Volume/Issue:: Volume 112: Issue 1-2

On an identity of Ramanujan over finitely generated domains

Authors:

Gabriella Hajdu

Gabriella Hajdu Institute of Mathematics and Computer Science, Faculty of Mechanical Engineering, Szent István University H-2103 Gödöllő, Páter K. u. 1., Hungary H-2103 Gödöllő, Páter K. u. 1., Hungary

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Lajos Hajdu

Lajos Hajdu Institute of Mathematics, University of Debrecen and the Number Theory Research Group of the Hungarian Academy of Sciences H-4010 Debrecen, P.O.B. 12, Hungary H-4010 Debrecen, P.O.B. 12, Hungary

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Pages:: 143–155

Online Publication Date:: 18 Jul 2006

Publication Date:: 18 Jul 2006

Article Category:: Research Article

DOI:: https://doi.org/10.1007/s10474-006-0070-4

Keywords:: Ramanujan's identity; functional equations; finitely generated domains

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Summary

We show that a well-known identity of Ramanujan admits only a bounded number of solutions over general finitely generated domains. The bound is explicit and uniform in the sense that it depends only on the dimensions of the domains involved. Our method is constructive, and opens up a possibility to determine the solutions in concrete instances. In some special cases all solutions are determined. Our results can also be considered as a continuation of some theorems of Z. Darczy and G. Hajdu, obtained over Z. We note that in case of Hossz's equation, similar results were obtained by several authors.

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Acta Mathematica Hungarica

Print ISSN:: 0236-5294

Online ISSN:: 1588-2632

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Acta Mathematica Hungarica
Language	English
Size	B5
Year of Foundation	1950
Volumes per Year	3
Issues per Year	6
Founder	Magyar Tudományos Akadémia
Founder's Address	H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher	Akadémiai Kiadó Springer Nature Switzerland AG
Publisher's Address	H-1117 Budapest, Hungary 1516 Budapest, PO Box 245. CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible Publisher	Chief Executive Officer, Akadémiai Kiadó
ISSN	0236-5294 (Print)
ISSN	1588-2632 (Online)