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On Negative Moments of the Riemann Zeta-Function

Published online by Cambridge University Press:  26 February 2010

S. M. Gonek
S. M. Gonek
Affiliation:
Department of Mathematics, University of Rochester, Rochester, NY 14627, U.S.A.
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Extract

The purpose of this paper is to take some first steps the investigation of the negative moments

where k>0 and 12, and the related discrete moments

where runs over the complex zeros of the zeta-function. We assume the Riemann hypothesis (RH) throughout; it then follows that Ik(, T) converges for every k > 0 when > but for no k = when =. We further note that Jk(T) is only defined for all T if all the zeros are simple and, in that case, Ik(, T) converges for all k<.

Type
Research Article
Information
Mathematika , Volume 36 , Issue 1 , June 1989 , pp. 71 - 88
Copyright
Copyright University College London 1989

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References

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