A zero density result for the Riemann zeta function

Volume 160 / 2013

Habiba Kadiri 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.

Authors

  • Habiba KadiriDepartment of Mathematics and Computer Science
    University of Lethbridge
    4401 University Drive
    Lethbridge, Alberta
    T1K 3M4 Canada
    e-mail

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