Gaps between zeros of the derivative of the Riemann ξ-function

Details Gaps between zeros of the derivative of the Riemann ξ-function Gaps between zeros of the derivative of the Riemann ξ-function

2009-03-24

arxiv.org/abs/0903.4006v1

Mathematics

Number Theory

15 pages

Scientific paper

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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