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Gaps between zeros of the derivative of the Riemann \xi-function

Number Theory 2012-11-06 v1

Abstract

Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of \xi'(s). We prove that a positive proportion of gaps are less than 0.796 times the average spacing and, in the other direction, a positive proportion of gaps are greater than 1.18 times the average spacing. We also exhibit the existence of infinitely many normalized gaps smaller (larger) than 0.7203 (1.5, respectively).

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Cite

@article{arxiv.0903.4006,
  title  = {Gaps between zeros of the derivative of the Riemann \xi-function},
  author = {H. M. Bui},
  journal= {arXiv preprint arXiv:0903.4006},
  year   = {2012}
}

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15 pages