Supremum of the function $S_1(t)$ on short intervals

Takahiro Wakasa

Supremum of the function $S_1(t)$ on short intervals

Number Theory 2013-11-19 v3

Authors: Takahiro Wakasa

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 result 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 for a lower bound.

Keywords

Riemann zeta-function function $S_1(t)$ supremum short intervals lower bound Omega-result Karatsuba and Korolev

Cite

@article{arxiv.1301.0057,
  title  = {Supremum of the function $S_1(t)$ on short intervals},
  author = {Takahiro Wakasa},
  journal= {arXiv preprint arXiv:1301.0057},
  year   = {2013}
}

Comments

15 pages

Related papers

View all related →