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 othaer
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).