Two complete and minimal systems associated with the zeros of the Riemann zeta function

Jean-François Burnol

Displaying similar documents to “Two complete and minimal systems associated with the zeros of the Riemann zeta function”

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.

On a two-variable zeta function for number fields

Jeffrey C. Lagarias, Eric Rains (2003)

Annales de l’institut Fourier

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This paper studies a two-variable zeta function $Z_{K} (w, s)$ attached to an algebraic number field $K$ , introduced by van der Geer and Schoof, which is based on an analogue of the Riemann-Roch theorem for number fields using Arakelov divisors. When $w = 1$ this function becomes the completed Dedekind zeta function ${\hat{ζ}}_{K} (s)$ of the field $K$ . The function is a meromorphic function of two complex variables with polar divisor $s (w - s)$ , and it satisfies the functional equation $Z_{K} (w, s) = Z_{K} (w, w - s)$ . We consider the special case $K = ℚ$ , where for $w = 1$ ...

Erratum - Zeta functions for the Riemann zeros

André Voros (2004)

Annales de l’institut Fourier

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A lower bound for the zeros of Riemann's zeta function on the critical line

Enrico Bombieri (1974-1975)

Séminaire Bourbaki

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Large gaps between consecutive zeros of the Riemann zeta-function. II

H. M. Bui (2014)

Acta Arithmetica

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Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.