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Thursday, January 18, 2018

**Abstract:** The celebrated theorem of Levinson (1974) states that more than 1/3 of the non-trivial zeros of the Riemann zeta-function are on the critical line. This result has been improved during the last 40 years by employing linear and first order terms of a mollifier as well as by using Kloostermania techniques for the error terms. In this work, we delineate how to improve all degrees of the most natural and powerful Dirichlet series (producing an arbitrarily perfect mollification) and we also present the best error terms available with our current technology of exponential sums by elucidating a conjecture of S. Feng. A new and modest % record is thereby achieved. Joint work with Kyle Pratt, Alexandru Zaharescu and Dirk Zeindler.

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