Some remarks on the differences between ordinates of consecutive zeta zeros. (English) Zbl 1455.11119

Ivić, Aleksandar

Funct. Approximatio, Comment. Math. 58, No. 1, 23-35 (2018).

Author’s abstract: If \(0 < \gamma_1 \le \gamma_2 \le \gamma_3 \le \ldots\) denote ordinates of complex zeros of the Riemann zeta-function \(\zeta(s)\), then several results involving the maximal order of \(\gamma_{n+1}-\gamma_n\) and the sum \[ \sum_{0<\gamma_n\le T}{(\gamma_{n+1}-\gamma_n)}^k \qquad(k>0) \] are proved.

Reviewer: Giovanni Coppola (Napoli)

MSC:

11M06

\(\zeta (s)\) and \(L(s, \chi)\)

Keywords:

Riemann zeta-function; consecutive zeta-zeros; large differences; Riemann hypothesis

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