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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Bibliographic Details
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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Summary: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.
ISSN:1364-5021