2018 年 72 巻 1 号 p. 35-69
In this paper, we establish the asymptotic formula for the second moment of the Riemann zeta-function twisted by a (Λ + 1)-piece mollifier which is a generalization of the two-piece mollifier considered by Bui, Conrey and Young [Acta. Arith. 150(1) (2011), 35-64]. As an application, we obtain a lower bound for the proportion of critical zeros of the Riemann zeta-function.