On a choice of the mollified function in the Levinson-Conrey method
  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. 
Sergei Preobrazhenskii and Tatyana Preobrazhenskaya
math.NT math.CV