Central European Journal of Mathematics

, Volume 9, Issue 1, pp 102–126

An explicit formula of Atkinson type for the product of the Riemann zeta-function and a Dirichlet polynomial

Research Article

DOI: 10.2478/s11533-010-0085-5

Cite this article as:
Ishikawa, H. & Matsumoto, K. centr.eur.j.math. (2011) 9: 102. doi:10.2478/s11533-010-0085-5

Abstract

We prove an explicit formula of Atkinson type for the error term in the asymptotic formula for the mean square of the product of the Riemann zeta-function and a Dirichlet polynomial. To deal with the case when coefficients of the Dirichlet polynomial are complex, we apply the idea of the first author in his study on mean values of Dirichlet L-functions.

Keywords

Riemann zeta-functionDirichlet polynomialAtkinson formula

MSC

11M0611M41

Copyright information

© © Versita Warsaw and Springer-Verlag Wien 2011

Authors and Affiliations

  1. 1.Faculty of EducationNagasaki UniversityNagasakiJapan
  2. 2.Graduate School of MathematicsNagoya UniversityNagoyaJapan