Pair correlation and twin primes revisited

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. Specifically, we prove that the ratios conjecture and the arithmetic correlations conjecture imply the same result. T...

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Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2016-10, Vol.472 (2194), p.1-11
Main Authors: Conrey, Brian, Keating, Jonathan P.
Format: Article
Language:English
Subjects:
Arithmetic
Grants
Heuristics
Mathematical moments
Matrix theory
Number theoretic functions
Number theory
Prime numbers
Ratios
Riemann zeta function
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Keating, Jonathan P.
description 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. Specifically, 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.
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source JSTOR Archival Journals and Primary Sources Collection; Royal Society Publishing Jisc Collections Royal Society Journals Read & Publish Transitional Agreement 2025 (reading list)
subjects Arithmetic
Grants
Heuristics
Mathematical moments
Matrix theory
Number theoretic functions
Number theory
Prime numbers
Ratios
Riemann zeta function
title Pair correlation and twin primes revisited
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