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

Sergei Preobrazhenskii, Tatyana Preobrazhenskaya

Published 2014-03-23, updated 2014-11-01Version 2

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 very slight improvement of Conrey's result: at least $40{.}883$% of the zeros of the Riemann zeta function are on the critical line. Our choice of the mollified function can be used to improve the recent results of Bui, Conrey and Young, and of Feng slightly, but the computations there are more complicated. Although the improvements are very modest, our construction might be useful in understanding good choices of the mollified function.