On the success and failure of Gram's Law and the Rosser Rule

Timothy Trudgian

Displaying similar documents to “On the success and failure of Gram's Law and the Rosser Rule”

More than 41% of the zeros of the zeta function are on the critical line

H. M. Bui, Brian Conrey, Matthew P. Young (2011)

Acta Arithmetica

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Zeros of the Riemann Zeta-function on the critical line.

D.R. Heath-Brown (1993)

Mathematische Zeitschrift

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A note on the zeros of the derivative of the Riemann zeta function near the critical line

Shaoji Feng (2005)

Acta Arithmetica

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More than two fifths of the zeros of the Riemann zeta function are on the critical line.

J.B. Conrey (1989)

Journal für die reine und angewandte Mathematik

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Small values of the Riemann zeta function on the critical line

Justas Kalpokas, Paulius Šarka (2015)

Acta Arithmetica

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We investigate real values of the Riemann zeta function on the critical line. We show that if Gram's points do not intersect with the ordinates of the nontrivial zeros of the Riemann zeta function then the Riemann zeta function takes arbitrarily small real values on the critical line.

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.

The zeros of Riemann's Zeta-Function on the critical line

G.H., and J.E. Littlewood Hardy (1921)

Mathematische Zeitschrift

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A note on moments of $ζ^{'} (1 / 2 + i γ)$ .

Laurinčikas, Antanas, Steuding, Jörn (2004)

Publications de l'Institut Mathématique. Nouvelle Série

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On large values of the Riemann zeta-function on short segments of the critical line

Maxim A. Korolev (2014)

Acta Arithmetica

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We obtain a series of new conditional lower bounds for the modulus and the argument of the Riemann zeta function on very short segments of the critical line, based on the Riemann hypothesis. In particular, we prove that for any large fixed constant A > 1 there exist(non-effective) constants T₀(A) > 0 and c₀(A) > 0 such that the maximum of |ζ (0.5+it)| on the interval (T-h,T+h) is greater than A for any T > T₀ and h = (1/π)lnlnln{T}+c₀.