On the Gram's Law in the Theory of Riemann Zeta Function

Abstract

Some statements concerning the distribution of imaginary parts of zeros of the Riemann zeta\,-function are established. These assertions are connected with so\,-called `Gram's law' or `Gram's rule'. In particular, we give a proof of several Selberg's formulae stated him without proof in his paper `The Zeta Function and the Riemann Hypothesis' (1946), and some of their equivalents.

35 pages, 1 figure