arXiv subjects
Publications and source records attributed to Jörn Steuding.
We investigate a modified Möbius $μ$-function which is related to an infinite product of shifted Riemann zeta-functions. We prove conditional and unconditional upper and lower bounds for its summatory function, and, finally, we discuss relations with Riemann's hypothesis.
We investigate the intersections of the curve $\mathbb{R}\ni t\mapsto ζ({1\over 2}+it)$ 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.
We examine statistical properties of the Calkin--Wilf tree and give number-theoretical applications.