On the mod-Gaussian convergence of a sum over primes

Details On the mod-Gaussian convergence of a sum over primes On the mod-Gaussian convergence of a sum over primes

2012-01-25

arxiv.org/abs/1201.5295v1

Mathematics

Number Theory

15 pages

Scientific paper

We prove mod-Gaussian convergence for a Dirichlet polynomial which
approximates $\log\zeta(1/2+it)$. Assuming the Riemann hypothesis we obtain an
explicit error term in Selberg's central limit theorem. On the other hand,
assuming the Riemann hypothesis again, we apply the theory of the Riemann
zeta-function to extend this mod-Gaussian convergence to the complex plane.

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