Twin prime correlations from the pair correlation of Riemann zeros

Author: 

Keating, J
Smith, D

Publication Date: 

13 August 2019

Journal: 

Journal of Physics A: Mathematical and Theoretical

Last Updated: 

2020-06-15T21:28:25.4+01:00

Issue: 

36

Volume: 

52

DOI: 

10.1088/1751-8121/ab3521

page: 

365201-365201

abstract: 

© 2019 IOP Publishing Ltd. We establish, via a heuristic Fourier inversion calculation, that the Hardy-Littlewood twin prime conjecture is equivalent to an asymptotic formula for the two-point correlation function of Riemann zeros at a height E on the critical line. Previously it was known that the Hardy-Littlewood conjecture implies the pair correlation formula, and we show that the reverse implication also holds. An averaged form of the Hardy-Littlewood conjecture is obtained by inverting the limit of the two-point correlation function and the precise form of the conjecture is found by including asymptotically lower order terms in the two-point correlation function formula.

Symplectic id: 

1055643

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article