Mod-poisson Convergence in Probability and Number Theory

  title={Mod-poisson Convergence in Probability and Number Theory},
  author={E. Kowalski and A. Nikeghbali},
Building on earlier work introducing the notion of “modGaussian” convergence of sequences of random variables, which arises naturally in Random Matrix Theory and number theory, we discuss the analogue notion of “mod-Poisson” convergence. We show in particular how it occurs naturally in analytic number theory in the classical Erdős-Kac Theorem. In fact, this case reveals deep connections and analogies with conjectures concerning the distribution of L-functions on the critical line, which belong… CONTINUE READING

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Publications referenced by this paper.
Showing 1-10 of 19 references


A. D. Barbour
Kowalski and A. Nikeghbali: Mod-discrete expansions, preprint • 2009
View 1 Excerpt


S. Gonek
Hughes and J. Keating: A hybrid Euler-Hadamard product for the Riemann zeta function, Duke Math. J. 136 • 2007
View 2 Excerpts

Soundararajan: Sieving and the Erdős-Kac Theorem, in “Equidistribution in Number Theory, An Introduction

K. A. Granville
View 2 Excerpts

Statistics of Prime Divisors in Function Fields

View 1 Excerpt

Logarithmic combinatorial structures: a probabilistic approach, E.M.S

R. Arratia, A. D. Barbour, S. Tavaré
View 1 Excerpt

Sharp constants in the Poisson approximation

B. Roos
Stat. Prob. Letters • 2001

Diaconis: New tests of the correspondence between unitary eigenvalues and the zeros of Riemann’s zeta function

P. M. Coram
J. Phys. A • 2000
View 1 Excerpt

Snaith: Random matrix theory and ζ(1/2 + it)

N.C.J.P. Keating
Commun. Math. Phys. 214, • 2000
View 1 Excerpt

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