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On Negative Moments of the Riemann Zeta-Function

  • S. M. Gonek (a1)
  • DOI:
  • Published online: 01 February 2010

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<.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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