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The mean value of the derivative of the Dedekind zeta-function of a real quadratic field

Published online by Cambridge University Press:  26 February 2010

Lenard Weinstein
Lenard Weinstein
Affiliation:
Department of Mathematics, Boston University, Boston, Massachusetts 02215
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Extract

Denote by ζk′(S), the derivative of the Dedekind zeta-function associated with the real quadratic field K. Then it is known that

where ζ(S) is the Riemann zeta-function, and L(s, x) is the Dirichlet L-series associated with the Legendre symbol X. Moreover, we have the functional equation

where D is the discriminant of K.

Type
Research Article
Information
Mathematika , Volume 24 , Issue 2 , December 1977 , pp. 226 - 236
Copyright
Copyright © University College London 1977

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References

1.Motohashi, Y.. “A note on the mean value of the Dedekind zeta-function of the quadratic field”, Math. Ann. 188 (1970) 123–127.CrossRefGoogle Scholar
2.Titchmarsh, E. C.. “The mean-value of the zeta-function on the critical line”, Proc. London Math. Soc, (2) 28 (1928), 137–150 (1928).CrossRefGoogle Scholar
3.Titchmarsh, E. C.. The theory of the Riemartn zeta-function, (Oxford, Clarendon Press, 1951).Google Scholar