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

H. M. Bui

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arXiv · 0903.4006

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

H. M. Bui

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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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H. M. Bui. 2009-03-24. Gaps between zeros of the derivative of the Riemann \xi-function. https://arxiv.org/abs/0903.4006

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