2 papers
math.NT2019
Twin prime correlations from the pair correlation of Riemann zeros
J. P. Keating, D. J. Smith
We establish, via a formal/heuristic Fourier inversion calculation, that the Hardy-Littlewood twin prime conjecture is equivalent to an asymptotic formula for the two-point correla…
math.NT2015
On the variance of sums of arithmetic functions over primes in short intervals and pair correlation for L-functions in the Selberg class
H. M. Bui, J. P. Keating, D. J. Smith
We establish the equivalence of conjectures concerning the pair correlation of zeros of -functions in the Selberg class and the variances of sums of a related class of arithmeti…