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W2897119932 abstract "We assume the Riemann Hypothesis in this paper. We settle a conjecture of Farmer and Ki in a stronger form. Roughly speaking we show that there is a positive proportion of small gaps between consecutive zeros of the zeta-function ζ(s) if and only if there is a positive proportion of zeros of ζ′(s) lying very closely to the half-line. Our work has applications to the Siegel zero problem. We provide a criterion for the non-existence of the Siegel zero, solely in terms of the distribution of the zeros of ζ′(s). Finally on the Riemann Hypothesis and the Pair Correlation Conjecture we obtain near optimal bounds for the number of zeros of ζ′(s) lying very closely to the half-line. Such bounds are relevant to a deeper understanding of Levinson's method, allowing us to place one-third of the zeros of the Riemann zeta-function on the half-line." @default.
W2897119932 created "2018-10-26" @default.
W2897119932 creator A5027276960 @default.
W2897119932 date "2014-06-01" @default.
W2897119932 modified "2023-09-24" @default.
W2897119932 title "Gaps between zeros of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:mi>ζ</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>and the distribution of zeros of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si2.gif overflow=scroll><mml:msup><mml:mrow><mml:mi>ζ</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:mi>s</…" @default.
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W2897119932 doi "https://doi.org/10.1016/j.aim.2014.02.010" @default.
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