On the value-distribution of the Riemann zeta-function on the critical line

2009/07/10 by Justas Kalpokas, Kalpokas, Justas, Jörn Steuding +1 · 2 citations
Mathematics · #Analytic Number Theory Research #Meromorphic and Entire Functions #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.0907.1910

Abstract

We investigate the intersections of the curve ℝ\ni t↦ ζ(1\over 2+it) with the real axis. We show that if the Riemann hypothesis is true, the mean-value of those real values exists and is equal to 1. Moreover, we show unconditionally that the zeta-function takes arbitrarily large real values on the critical line.

Cited by

• Non universality on the critical line
• Hardy's function Z(t) - results and problems

Related

• Value-distribution of the Riemann zeta-function and related functions near the critical line
• The a-values of the Riemann zeta function near the critical line
• On small values of the Riemann zeta-function on the critical line and gaps between zeros
• Extreme values of the Riemann zeta function at its critical points in the critical strip
• Almost all of the nontrivial zeros of the Riemann zeta-function are on the critical line