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Hung Manh Bui
Gaps between zeros of the derivative of the Riemann $\xi $-function
Journal de théorie des nombres de Bordeaux, 22 no. 2 (2010), p. 287-305, doi: 10.5802/jtnb.716
Article PDF | Reviews MR 2769063 | Zbl 1223.11103
Class. Math.: 11M26, 11M06

Résumé - Abstract

Assuming the Riemann hypothesis, we investigate the distribution of gaps between the zeros of $\xi ^{\prime}(s)$. 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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