Pair correlation of zeros of the zeta function.
P.X. Gallagher (1985)
Journal für die reine und angewandte Mathematik
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P.X. Gallagher (1985)
Journal für die reine und angewandte Mathematik
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D.A. Goldston (1988)
Journal für die reine und angewandte Mathematik
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J.B. Conrey (1989)
Journal für die reine und angewandte Mathematik
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P.D.T.A. Elliott (1972)
Journal für die reine und angewandte Mathematik
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Akio Fujii (1979)
Journal für die reine und angewandte Mathematik
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Tsz Ho Chan (2004)
Acta Arithmetica
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H. M. Bui (2014)
Acta Arithmetica
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Assuming the Riemann Hypothesis we show that there exist infinitely many consecutive zeros of the Riemann zeta-function whose gaps are greater than 2.9 times the average spacing.
S. Chowla, A. Selberg (1967)
Journal für die reine und angewandte Mathematik
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Robert Spira (1972)
Journal für die reine und angewandte Mathematik
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Laurinčikas, Antanas, Steuding, Jörn (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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D.R. Heath-Brown, J.B. Conrey (1985)
Journal für die reine und angewandte Mathematik
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Shaoji Feng (2005)
Acta Arithmetica
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Riad Masri (2007)
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.
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.