Ramunas Garunkstis: On the zeros of the Riemann zeta-function

Abstract:

We present several results about zeros of the Riemann zeta-function \(\zeta(s)\). One of them states that \(\zeta(s)\) and its derivative have the same number of zeros in small areas located to the left of the critical line and near it. This is related to similar investigations by Levinson and Montgomery. Futher, we consider the mean value of \(\zeta(s)\) over its shifted nontrivial zeros. This topic was started by Gonek.