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    Milinovich, M. B. and Ng, N. 2013. Lower Bounds for Moments of  '( ). International Mathematics Research Notices,


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    Hughes, C P 2003. Random matrix theory and discrete moments of the Riemann zeta function. Journal of Physics A: Mathematical and General, Vol. 36, Issue. 12, p. 2907.


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    Laurinčikas, A. 2000. A remark on negative moments of the Riemann zeta-function. Lithuanian Mathematical Journal, Vol. 40, Issue. 1, p. 23.


    Farmer, David W. 1993. Long mollifiers of the Riemann Zeta-function. Mathematika, Vol. 40, Issue. 01, p. 71.


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On Negative Moments of the Riemann Zeta-Function

  • S. M. Gonek (a1)
  • DOI: http://dx.doi.org/10.1112/S0025579300013589
  • Published online: 01 February 2010
Abstract

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