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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
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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.

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

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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