Description
Abstract: There are several methods to obtain a lower bound for the mean value of the absolute value of the remainder term of the prime number formula as function of a hypothetical zero of the Riemann Zeta function off the critical line. (The case when the Riemann Hypothesis is true can be treated easier.) The most efficient ones include results of Knapowski-Turán, Sz. Gy. Révész , and the author, proved by several different methods
The result to be proved in the lecture provides (again with an other method) a quite good lower bound and it has the good feature (which is useful in further applications too) that instead of the whole interval [0,X] it gives a good lower bound for the average on [F(X), X] with logF(X) close to logX (that is on "short" intervals measured with the logarithmic scale)
For Zoom access please contact Andras Biro (biro.andras[a]renyi.hu).