Simple Zeros of the Riemann Zeta-Function

Conrey, J. Brian; Ghosh, Amit; Gonek, S. M.

doi:10.1112/s0024611598000306

Cited by 60 publications

(84 citation statements)

References 8 publications

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“…The number of γ ≤ T was proven by Riemann and von Mangoldt to equal T 2π log T 2πe + O(log T ). Chris Hughes [22][23][24] has conjectured a formula for the leading term of where a, c > 0, a sum which was considered in Farmer's paper [9,14]. Farmer's conjecture for this sum is…”

Section: Discrete Moments Of ζmentioning

confidence: 99%

Autocorrelation of ratios of $L$-functions

Conrey

Farmer

Zirnbauer

2008

Communications in Number Theory and Physics

129

232

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Section: Discrete Moments Of ζmentioning

confidence: 99%

Autocorrelation of ratios of $L$-functions

Conrey

Farmer

Zirnbauer

2008

Communications in Number Theory and Physics

129

232

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“…In 1998, under the assumption of the Riemann Hypothesis and the Generalized Lindelöf Hypothesis, Conrey, Ghosh and Gonek (see [7]) proved that more than 84.56% of the zeros of the Riemann zeta function are distinct. Recently, Bui and Heath-Brown (see [4]) improved the result, they showed that at least 84.665% of the zeros of the Riemann zeta-function are distinct, assuming the Riemann Hypothesis.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Zero distribution of Dirichlet L-functions

Wu²

2016

Ann. Acad. Sci. Fenn. Math.

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“…It would be a major advance to be able to prove that almost all the zeros are simple, even on RH. Conrey, Ghosh, and Gonek [6] have proved using a different method that assuming RH and the Generalized Lindelöf Hypothesis,…”

Section: Application To Simple Zeros and Small Gaps Between Zerosmentioning

confidence: 99%

Notes on pair correlation of zeros and prime numbers

Goldston¹

2005

Recent Perspectives in Random Matrix Theory and Number Theory

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These notes are based on my four lectures given at the Newton Institute in April 2004 during the Recent Perspectives in Random Matrix Theory and Number Theory Workshop. Their purpose is to introduce the reader to the analytic number theory necessary to understand Montgomery's work on the pair correlation of the zeros of the Riemann zeta-function and subsequent work on how this relates to prime numbers. A very brief introduction to Selberg's work on the moments of S(T ) is also given.

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Simple Zeros of the Riemann Zeta-Function

Cited by 60 publications

References 8 publications

Autocorrelation of ratios of $L$-functions

Autocorrelation of ratios of $L$-functions

Zero distribution of Dirichlet L-functions

Notes on pair correlation of zeros and prime numbers

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