Gaps between zeros of the derivative of the Riemann ξ-function
Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 2, pp. 287-305.

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).

En supposant l’hypothèse de Riemann, on examine la distribution d’écarts entre les zéros du ξ (s). On démontre qu’une proportion positive d’écarts sont inférieurs à 0.796 fois l’écart moyen et que dans l’autre direction, une proportion positive d’écarts sont 1.18 fois supérieurs à l’écart moyen. On montre également l’existence d’un nombre infini d’écarts normalisés qui sont inférieurs (supérieurs) à 0.7203 (respectivement 1.5).

Received:
Revised:
Published online:
DOI: 10.5802/jtnb.716
Classification: 11M26,  11M06
Hung Manh Bui 1

1 Mathematical Institute University of Oxford Oxford, OX1 3LB England
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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, Volume 22 (2010) no. 2, pp. 287-305. doi : 10.5802/jtnb.716. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.716/

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