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We introduce a new mollifier and apply the method of Levinson and Conrey to prove that at least 41.28% of the zeros of the Riemann zeta function are on the critical line. The method may also be used to improve other results on zeros relate to the Riemann zeta function, as well as conditional results on prime gaps.
Berndt, Levinson and Montgomery investigated the distribution of nonreal zeros of derivatives of the Riemann zeta function, including the number of zeros up to a height T and the distribution of the real part of nonreal zeros. In this paper we obtain sharper estimates for the error terms of their results in the case of the first derivative of the Riemann zeta function, under the truth of the Riemann...
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