A zero density result for the Riemann zeta function
Volume 160 / 2013
Acta Arithmetica 160 (2013), 185-200
MSC: Primary 11M06, 11M26; Secondary 11Y35.
DOI: 10.4064/aa160-2-6
Abstract
We prove an explicit bound for $N(\sigma ,T)$, the number of zeros of the Riemann zeta function satisfying $\mathfrak {Re}\,s\ge \sigma $ and $0 \le \mathfrak {Im}\, s \le T$. This result provides a significant improvement to Rosser's bound for $N(T)$ when used for estimating prime counting functions.
