Abstract
It is known that the Riemann hypothesis is true if and only if ▪ belongs to the Nyman-Beurling space, where ▪ denotes the characteristic function on the unit interval. Moreover, Báez-Duarte, Balazard, Landreau, and Saias provided a lower bound for the distance between ▪ and the subspaces of the Nyman-Beurling space. In this paper, we extend the result of Báez-Duarte et al. by considering more general characteristic functions. In addition, we give some applications and raise several questions related to the Riemann hypothesis.
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