SUPREMUM OF THE FUNCTION S_1(t) ON SHORT INTERVALS

Author:

Takahiro~Wakasa

2010 Mathematics Subject Classification:

11M06.

Keywords:

argument, Riemann zeta-function.

Abstract:

We prove a lower bound on the supremum of the function S_1(T) on short intervals defined by the integration of the argument of the Riemann zeta-function. The same type of results on the supremum of S(T) have already been obtained by Karatsuba and Korolev. Our result is based on the idea of the paper of Karatsuba and Korolev. Also, we show an improved Omega-result of Selberg's result for a lower bound.

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Waka_2014

Vol. 9 (17), 2014