A Note on the Distribution of the Zeros of the Zeta-Function

Abstract

on the other hand, where pi = pi + iy1, P2 = /2 + iy2, . . . denote. the zeros of g(s) in the upper half-plane. While for the purposes of Littlewood only a consequence of the Dirichlet approximation theorem is relevant, it seems to be worth while to determine the asymptotic cyclical distribution of (1). The object of the present note is to point out the fact that the sequence (1) is asymptotically equidistributed t to modulus c, where c is any non-vanishing real number. In order to simplify the formulae we shall choose c = 1; it will be clear that the proof holds for any c. We have to prove that