Hostname: page-component-7dd5485656-j7khd Total loading time: 0 Render date: 2025-10-30T18:52:37.879Z Has data issue: false hasContentIssue false
  • English
  • Français

On a problem about the Epstein zeta-function

Published online by Cambridge University Press:  24 October 2008

Veikko Ennola
Veikko Ennola
Affiliation:
University of Turku, Finland
Get access Rights & Permissions [Opens in a new window]

Extract

1. Let

be a positive definite binary quadratic form with determinant αβ − δ2 = 1. A special form of this kind is

We consider the Epstein zeta-function

the series converging for . The function Zh(s) can be analytically continued over the whole s-plane and it is regular except for a simple pole with residue π at s = 1.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 855 - 875
Copyright
Copyright © Cambridge Philosophical Society 1964

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

(1)Cassels, J. W. S.On a problem of Rankin about the Epstein zeta-function. Proc. Glasgow Math. Assoc. 4 (1959), 73–80.CrossRefGoogle Scholar
(2)Ennola, V. A lemma about the Epstein zeta-function. Proc. Glasgow Math. Assoc. (to appear).Google Scholar
(3)Epstein, Paul. Zur Theorie allgemeiner Zetafunctionen, I, II. Math. Ann. 56 (1903), 615–644; 63 (1907), 205–216.Google Scholar
(4)Rankin, R. A.A minimum problem for the Epstein zeta-function. Proc. Glasgow Math. Assoc. 1 (1953), 149–158.CrossRefGoogle Scholar