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

Hung Manh Bui — 2010

Journal de Théorie des Nombres de Bordeaux

Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of $ξ^{'} (s)$ . 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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Gaps between zeros of the derivative of the Riemann ξ -function

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