Ein mengentheoretischer Satz über die Gleichverteilung modulo Eins
In this paper we demonstrate the relation between uniform distribution modulo 1 of the sequence cpα, p prime, and the zero free regions of the Riemann zeta function.
Let be the quotient group of the -adele ring of an algebraic number field by the discrete group of -integers. Given a probability measure on and an endomorphism of , we consider the relation between uniform distribution of the sequence for -almost all and the behavior of relative to the translations by some rational subgroups of . The main result of this note is an extension of the corresponding result for the -dimensional torus due to B. Host.