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Abstract : We review generalized zeta functions built over the Riemann zeros in short: "superzeta" functions.


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They are symmetric functions of the zeros that display a wealth of explicit properties, fully matching the much more elementary Hurwitz zeta function. As a concrete application, a superzeta function enters an integral repre-sentation for the Keiper—Li coefficients, whose large-order behavior thereby becomes computable by the method of steepest descents; then the dominant saddle-point en-tirely depends on the Riemann Hypothesis being true or not, and the outcome is a sharp exponential-asymptotic criterion for the Riemann Hypothesis that only refers to the large-order Keiper—Li coefficients.

Riemann zeta function

Document type : Conference papers. Domain : Mathematics [math]. Zeta functions over zeros of Zeta functions and an exponential-asymptotic view of the Riemann Hypothesis. If you originally registered with a username please use that to sign in.

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Riemann Zeta Function

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    ON THE ZEROS OF THE RIEMANN ZETA FUNCTION | The Quarterly Journal of Mathematics | Oxford Academic

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