# Fractional parts and their relations to the values of the Riemann zeta function

Arabian Journal of Mathematics, Sep 2017

A well-known result, due to Dirichlet and later generalized by de la Vallée–Poussin, expresses a relationship between the sum of fractional parts and the Euler–Mascheroni constant. In this paper, we prove an asymptotic relationship between the summation of the products of fractional parts with powers of integers on the one hand, and the values of the Riemann zeta function, on the other hand. Dirichlet’s classical result falls as a particular case of this more general theorem.

This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2Fs40065-017-0184-2.pdf

Ibrahim M. Alabdulmohsin. Fractional parts and their relations to the values of the Riemann zeta function, Arabian Journal of Mathematics, 2017, 1-8, DOI: 10.1007/s40065-017-0184-2