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Notes on two lemmas concerning the Epstein zeta-function

Published online by Cambridge University Press:  18 May 2009

P. H. Diananda
P. H. Diananda
Affiliation:
University of Singapore
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1. We use Cassels's notation and define h (m, n), Q (m, n), Zh (s), Zh (1) – ZQ (1) and G (x, y) as in [1]. Rankin [5] proved that the Epstein zeta-function Zh (s) satisfies, for s ≧ 1·035, the

THEOREM. For s > 0, Zh (s) — ZQ (s) ≧ 0 with equality if and only ifh is equivalent to Q. Rankin then asked whether the theorem is true for all s > 1. Cassels [1] answered this question in the affirmative and proved further that the theorem is true for all s > 0.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 4 , July 1964 , pp. 202 - 204
Copyright
Copyright © Glasgow Mathematical Journal Trust 1964

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.Cassels, J. W. S., Corrigendum to [1], Proc. Glasgow Math. Assoc. 6 (1963), 116.Google Scholar
3.Emersleben, O., Review of [1], Zbl. Math.Google Scholar
4.Ennola, Veikko, A lemma about the Epstein zeta-function, Proc. Glasgow Math. Assoc. 6 (1964), 198–201.CrossRefGoogle Scholar
5.Rankin, R. A., A minimum problem for the Epstein zeta-function, Proc. Glasgow Math. Assoc. 1 (1953), 149–158.CrossRefGoogle Scholar