On the large values of the Riemann zeta-function on short segments of the critical line

TL;DR

This paper establishes new conditional lower bounds for the Riemann zeta function's magnitude and argument on short segments of the critical line, assuming the Riemann hypothesis, and addresses previous typos and corrections.

Contribution

It provides the first conditional lower bounds for the zeta function on very short segments, solving a problem posed by A.A. Karatsuba.

Findings

Conditional lower bounds for the zeta function's modulus

Conditional lower bounds for the argument of the zeta function

Resolution of a problem posed by A.A. Karatsuba

Abstract

In this paper, we obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, the conditional solution of one problem of A.A.Karatsuba is given. Some typos of the previous versions are corrected (in particular, the important remark of Prof. Yan Fyodorov is taken into account). The reference to the grant of Russian Scientific Fund is also added.