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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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