Pair correlation of zeros of the zeta function.
P.X. Gallagher (1985)
Journal für die reine und angewandte Mathematik
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Displaying similar documents to “On the pair correlation conjecture for zeros of the Riemann zeta-function.”
Pair correlation of zeros of the zeta function.
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Pair correlation of the zeros of the Riemann zeta function in longer ranges
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More than two fifths of the zeros of the Riemann zeta function are on the critical line.
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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.
Gaps between primes, and the pair correlation of zeros of the zeta-function
D. Heath-Brown (1982)
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D.R. Heath-Brown, J.B. Conrey (1985)
Journal für die reine und angewandte Mathematik
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P.D.T.A. Elliott (1972)
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Akio Fujii (1979)
Journal für die reine und angewandte Mathematik
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A zero density result for the Riemann zeta function
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.