Displaying similar documents to “Riemann's Hypothesis”

Zeta functions for the Riemann zeros

André Voros (2003)

Annales de l’institut Fourier

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A family of Zeta functions built as Dirichlet series over the Riemann zeros are shown to have meromorphic extensions in the whole complex plane, for which numerous analytical features (the polar structures, plus countably many special values) are explicitly displayed.

Some problems on mean values of the Riemann zeta-function

Aleksandar Ivić (1996)

Journal de théorie des nombres de Bordeaux

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Several problems and results on mean values of ζ ( s ) are discussed. These include mean values of | ζ ( 1 2 + i t ) | and the fourth moment of | ζ ( σ + i t ) | for 1 / 2 < σ < 1 .

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

Hung Manh Bui (2010)

Journal de Théorie des Nombres de Bordeaux

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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).