L. Arguin

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20012026

most citedMaximum of the characteristic polynomial of random unitary matrices

103 citations · 478 across the 40 of their papers we have counts for

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Showing 2024 · math.NTShow all

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math.NT2024

Upper Bounds on Large Deviations of Dirichlet $L$ -functions in the $q$ -aspect

Louis-Pierre Arguin, Nathan Creighton

We prove a result on the large deviations of the central values of even primitive Dirichlet $L$ -functions with a given modulus. For $V \sim α lo g lo g q$ with $0 < α < 1$ , we show that \…

math.NT2024

The Fyodorov--Hiary--Keating Conjecture on Mesoscopic Intervals

Louis-Pierre Arguin, Jad Hamdan

We derive precise upper bounds for the maximum of the Riemann zeta function on a typical short interval of the critical line. We show that for fixed $θ \in (- 1, 0]$ , large $T$ , and $y…

math.NT2024

Lower Bounds for the Large Deviations of Selberg's Central Limit Theorem

Louis-Pierre Arguin, Emma Bailey

Let $δ > 0$ and $σ = \frac{1}{2} + \frac{δ}{l o g T}$ . We prove that, for any $α > 0$ and $V \sim α lo g lo g T$ as $T \to \infty$ , $\frac{1}{T}\text{meas}\big\{t\in [T,2T]: \log|ζ(σ+\rm{i} τ)|>…

Upper Bounds on Large Deviations of Dirichlet L-functions in the q-aspect

The Fyodorov--Hiary--Keating Conjecture on Mesoscopic Intervals

Lower Bounds for the Large Deviations of Selberg's Central Limit Theorem

Upper Bounds on Large Deviations of Dirichlet $L$ -functions in the $q$ -aspect