Zeros of the Riemann zeta-function and its universality
Volume 181 / 2017
Acta Arithmetica 181 (2017), 127-142
MSC: Primary 11M06.
DOI: 10.4064/aa8583-5-2017
Published online: 17 November 2017
Abstract
Let $0 \lt \gamma_1\leq \gamma_2 \leq\cdots$ be the imaginary parts of non-trivial zeros of the Riemann zeta-function $\zeta(s)$. Using the Montgomery conjecture (its weaker form) on the pair correlation of the sequence $\{\gamma_k\}$, we show that analytic functions of a wide class can be approximated by shifts $\zeta(s+i\gamma_k)$.
