Questions around the nontrivial zeros of the Riemann zeta-function. Computations and classifications

Abstract

We study the sequence of nontrivial zeros of the Riemann zeta-function with respect to sequences of zeros of other related functions, namely, the Hurwitz zeta-function and the derivative of Riemann's zeta-function. Finally, we investigate connections of the nontrivial zeros with the periodic zeta-function. On the basis of computation we derive several classifications of the nontrivial zeros of the Riemann zeta-function and stateproblems which mightbe ofinterestfor abetter understanding of the distribution of those zeros.

Keywords

• Riemann zeta-function
• Hurwitz zeta-function
• periodic zeta-function
• nontrivial zeros