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math.PR2012★ 19 cited
A central limit theorem for the zeroes of the zeta function
Brad Rodgers
On the assumption of the Riemann hypothesis, we generalize a central limit theorem of Fujii regarding the number of zeroes of Riemann's zeta function that lie in a mesoscopic inter…
math.NT2012★ 12 cited
Macroscopic pair correlation of the Riemann zeroes for smooth test functions
Brad Rodgers
On the assumption of the Riemann hypothesis, we show that over a class of sufficiently smooth test functions, a measure conjectured by Bogomolny and Keating coincides to a very sma…