On the Zeros of the Error Term for the Mean Square of | ζ(½ + it) |

Abstract

Abstract.Let E(T) denote the error term in the asymptotic formula for f Jo 2 2 dt.The function E(T) has mean value n. By tn we denote the n\X\ zero of E(T) -n . Several results concerning tn are obtained, including tn+x -tn < i iltn . An algorithm is presented to compute the zeros of E(T)-n below a given bound. For T < 500000, 42010 zeros of E(T)-n were found. Various tables and figures are given, which present a selection of the computational results.

The Riemann hypothesis: a resource for the afficionado and virtuoso alike

“…Numerical investigations concerning E 1 (T ) were carried out by H.J.J. te Riele and the author [29].…”