Pair correlation and twin primes revisited

Brian Conrey; Jon P Keating

doi:10.1098/rspa.2016.0548

Pair correlation and twin primes revisited

Brian Conrey, Jon P Keating

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Abstract

We establish a connection between the conjectural two-over-two ratios formula for the Riemann zeta-function and a conjecture concerning correlations of a certain arithmetic function. Speci cally, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. This casts a new light on the underpinnings of the ratios conjecture, which previously had been motivated by analogy with formulae in random matrix theory and by a heuristic recipe.

Original language	English
Article number	20160548
Number of pages	11
Journal	Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume	472
Issue number	2194
Early online date	5 Oct 2016
DOIs	https://doi.org/10.1098/rspa.2016.0548
Publication status	Published - Oct 2016

Keywords

pair correlation
random matrix theory
twin primes

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10.1098/rspa.2016.0548

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This is the final published version of the article (version of record). It first appeared online via The Royal Society at http://rspa.royalsocietypublishing.org/content/472/2194/20160548. Please refer to any applicable terms of use of the publisher.
Final published version, 358 KBLicence: CC BY

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L-functions and modular forms
Keating, J. P. & Booker, A. R.
1/06/13 → 30/09/19
Project: Research

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KW - random matrix theory

KW - twin primes

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M3 - Article (Academic Journal)

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Pair correlation and twin primes revisited

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Keywords

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L-functions and modular forms

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