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

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).

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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DOI : https://doi.org/10.5802/jtnb.716
Classification : 11M26,  11M06
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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, Tome 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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