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arXiv · 1403.5786

On a choice of the mollified function in the Levinson-Conrey method

Sergei Preobrazhenskii·Tatyana Preobrazhenskaya
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Abstract

Motivated by a functional property of the Riemann zeta function, we consider a new form of the mollified function in the Levinson-Conrey method. As an application, we give the following slight improvement of Feng's result: assuming Feng's condition on the lengths of the mollifier at least 41.2948% of the zeros of the Riemann zeta function are on the critical line. The construction may lead to further improvements as one increases the number of terms in Feng's mollifier.

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Sergei Preobrazhenskii, Tatyana Preobrazhenskaya. 2014-03-23. On a choice of the mollified function in the Levinson-Conrey method. https://arxiv.org/abs/1403.5786

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