AN EXPLICIT FORMULA OF ATKINSON TYPE FOR THE PRODUCT OF \zeta(s) AND A DIRICHLET POLYNOMIAL. II

Author:

Hideaki~ISHIKAWA, Kohji~MATSUMOTO

2010 Mathematics Subject Classification:

11M06.

Keywords:

Atkinson formula, Dirichlet polynomial, mean square, Riemann zeta-function, \Omega-result.

Abstract:

In our former paper, we proved a formula of Atkinson type for the mean square I(T,A) of the product of the Riemann zeta-function and a Dirichlet polynomial A(s).   Using that formula, in the present paper, we prove an \Omega-result on the difference between I(T,A) and I(T,\overline{A}), where \overline{A}(s) is the Dirichlet polynomial whose coeffecients are complex conjugates of those of A(s).

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Ishi-Mats-2013

Vol. 8 (16), 2013