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On the zeros of Epstein's zeta function

Published online by Cambridge University Press:  26 February 2010

H. M. Stark
H. M. Stark
Affiliation:
The Department of Mathematics, The University of Michigan, Ann Arbor, Michigan, U.S.A.
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Extract

Let Q(x, y) = ax2 + bxy + cy2 be a positive definite quadratic form with discriminant d = b2 – 4ac. The Epstein zeta function associated with Q is given by

where Σ′ means the sum is over all pairs (x, y) of integers not both zero, and as usual, s = σ + it.

Type
Research Article
Information
Mathematika , Volume 14 , Issue 1 , June 1967 , pp. 47 - 55
Copyright
Copyright © University College London 1967

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References

1.Bateman, P. T. and Grosswald, E., “On Epstein's zeta function”, Ada Arithmetica, 9 (1964), 365–373.CrossRefGoogle Scholar
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