Dirichlet L-functions on the critical line and multiplicative chaos

2025/06/19 by Vihko, Sami · 1 citation
#11M06 #60F17 #60G20 #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR)

paper · doi:10.48550/arxiv.2506.16115

Abstract

In this paper we prove that the Dirichlet L-functions L(1/2+ix,χ_q), where χ_q is uniformly random Dirichlet character modulo q and x∈ ℝ, converges to a random Schwartz distribution ζ_rand, which is related to (complex) Gaussian multiplicative chaos. This is the same limiting object that appeared in [34], where the authors proved that the random shifts of the Riemann zeta function on the critical line ζ(1/2+ix+iωT), where ω∼ Unif ([0,1]), converge as T→ ∞.

Citations

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Cited by

• On the error term of the fourth moment of the Riemann zeta-function

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• High points of a random model of the Riemann-zeta function and Gaussian multiplicative chaos