A zero density result for the Riemann zeta function

Habiba Kadiri

Type: Article

Publication Date: 2013-01-01

Citations: 18

DOI: https://doi.org/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 $N(T)$ whe

Locations

Acta Arithmetica - View - PDF
arXiv (Cornell University) - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF

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+	Autour de la fonction qui compte le nombre de nombres premiers	1998	Pierre Dusart
+ PDF Chat	Approximate formulas for some functions of prime numbers	1962	J. Barkley Rosser Lowell Schoenfeld
+	Minor arcs for Goldbach's problem	2012	H. A. Helfgott
+ PDF Chat	Sharper bounds for the Chebyshev functions 𝜃(𝑥) and 𝜓(𝑥). II	1976	Lowell Schoenfeld
+	Estimates of Some Functions Over Primes without R.H.	2010	Pierre Dusart
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+	An improved upper bound for the argument of the Riemann zeta-function on the critical line II	2013	Timothy S. Trudgian
+ PDF Chat	Primes in arithmetic progressions	1996	Olivier Ramaré Robert Rumely
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+ PDF Chat	Über die Nullstellen der Riemannschen Zetafunktion	1916	Robin Backlund