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arXiv · 1306.0856

On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis

H. M. Bui·S. J. Lester·M. B. Milinovich
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Abstract

Balazard, Saias, and Yor proved that the Riemann Hypothesis is equivalent to a certain weighted integral of the logarithm of the Riemann zeta-function along the critical line equaling zero. Assuming the Riemann Hypothesis, we investigate the rate at which a truncated version of this integral tends to zero, answering a question of Borwein, Bradley, and Crandall and disproving a conjecture of the same authors. A simple modification of our techniques gives a new proof of a classical Omega theorem for the function S(t) in the theory of the Riemann zeta-function.

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H. M. Bui, S. J. Lester, M. B. Milinovich. 2013-06-04. On Balazard, Saias, and Yor's equivalence to the Riemann Hypothesis. https://doi.org/10.1016/j.jmaa.2013.06.063

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