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ON GOOD UNIVERSALITY AND THE RIEMANN HYPOTHESIS

Abstract : We use subsequence and moving average ergodic theorems applied to Boole's transformation and its variants and their invariant measures on the real line to give new characterisations of the Lindelhöf Hypothesis and the Riemann hypothesis. These ideas are then used to study the value distribution of Dirichlet L series, and the zeta functions of Dedekind, Hurwitz and Riemann and their derivatives. This builds on earlier work of R. L. using Birkhoff's ergodic theorem and probability theory.
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https://hal.archives-ouvertes.fr/hal-02860568
Contributor : Jean-Louis Verger-Gaugry <>
Submitted on : Monday, April 5, 2021 - 10:40:05 PM
Last modification on : Thursday, April 8, 2021 - 3:23:44 AM

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  • HAL Id : hal-02860568, version 2
  • ARXIV : 2006.05116

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Jean-Louis Verger-Gaugry, Radhakrishnan Nair, Michel Weber. ON GOOD UNIVERSALITY AND THE RIEMANN HYPOTHESIS. Advances in Mathematics, Elsevier, In press. ⟨hal-02860568v2⟩

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