Gaps between primes, and the pair correlation of zeros of the zeta-function

D. Heath-Brown

Displaying similar documents to “Gaps between primes, and the pair correlation of zeros of the zeta-function”

Pair correlation of the zeros of the Riemann zeta function in longer ranges

Tsz Ho Chan (2004)

Acta Arithmetica

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Large gaps between consecutive zeros of the Riemann zeta-function. II

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.

More precise Pair Correlation Conjecture on the zeros of the Riemann zeta function

Tsz Ho Chan (2004)

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On the pair correlation conjecture for zeros of the Riemann zeta-function.

D.A. Goldston (1988)

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An Asymptotic Formula for a sum Involving Zeros of the Riemann Zeta-function

Yuichi Kamiya, Masatoshi Suzuki (2004)

Publications de l'Institut Mathématique

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Pair correlation of zeros of the zeta function.

P.X. Gallagher (1985)

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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.