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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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.
Shaoji Feng (2005)
Acta Arithmetica
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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.
Ramachandra, K., Sankaranarayanan, A. (1991)
Publications de l'Institut Mathématique. Nouvelle Série
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R. R. Hall (2006)
Acta Arithmetica
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A. Laurinčikas (1990)
Acta Arithmetica
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Norman Levinson (1972)
Acta Arithmetica
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André Voros (2004)
Annales de l’institut Fourier
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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.
Tsz Ho Chan (2004)
Acta Arithmetica
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