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On a problem of Rankin about the Epstein zeta-function

Published online by Cambridge University Press:  18 May 2009

J. W. S. Cassels
J. W. S. Cassels
Affiliation:
Trinity College, Cambridge
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Let

be a positive definite quadratic form with determinant αβ−X2 = 1. A special form of this kind is

We consider the Epstein zeta-function

the series converging for s > 1. For s ≥ 1·035 Rankin [1] proved the following

STatement R.

The sign of equality is needed only when h is equivalent to Q.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 4 , Issue 2 , July 1959 , pp. 73 - 80
Copyright
Copyright © Glasgow Mathematical Journal Trust 1959

References

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3.Deuring, M., Zeta-funktionen quadratischer Formen, J. fur reine u, angew. Math. 172 (1935), 226–252.CrossRefGoogle Scholar
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