Pair correlation of the zeros of the Riemann zeta function in longer ranges
Tsz Ho Chan (2004)
Acta Arithmetica
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Tsz Ho Chan (2004)
Acta Arithmetica
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Laurinčikas, Antanas, Steuding, Jörn (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Yuichi Kamiya, Masatoshi Suzuki (2004)
Publications de l'Institut Mathématique
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J. Kaczorowski, A. Perelli (2008)
Acta Arithmetica
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Csordas, George, Yang, Chung-Chun (2003)
Southwest Journal of Pure and Applied Mathematics [electronic only]
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Shaoji Feng (2005)
Acta Arithmetica
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Masatoshi Suzuki (2015)
Acta Arithmetica
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We show that the density functions of nearest neighbor spacing distributions for the zeros of the real or imaginary part of the Riemann xi-function on vertical lines are described by the M-function which appears in value distribution of the logarithmic derivative of the Riemann zeta-function on vertical lines.
D.R. Heath-Brown (1993)
Mathematische Zeitschrift
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André Voros (2004)
Annales de l’institut Fourier
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D. Heath-Brown (1982)
Acta Arithmetica
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Timothy Trudgian (2011)
Acta Arithmetica
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Tsz Ho Chan (2004)
Acta Arithmetica
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D.A. Goldston (1988)
Journal für die reine und angewandte Mathematik
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Habiba Kadiri (2013)
Acta Arithmetica
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We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.