Noam Pirani

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20212026

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math.NT2026

Closed geodesics in homology classes modulo sublattices

Noam Pirani

Let $M$ be a Weil-Petersson random hyperbolic surface of genus $g$ , and let $Γ \subset Z^{2 g}$ be a lattice of prime index $q$ . We study the distribution of primitive close…

math.NT2024

Traces of powers of random matrices over local fields

Noam Pirani

Let $M$ be chosen uniformly at random w.r.t. the Haar measure on the unitary group $U_{n}$ , the unitary symplectic group $U S p_{2 n}$ or the orthogonal group $O_{n}$ . Diaconis and Shasha…

math.NT2022

Abhyankar's Affine Arithmetic Conjecture for the Symmetric and Alternating Groups

Alexei Entin, Noam Pirani

We prove that for any prime $p > 2$ , $q = p^{ν}$ a power of $p$ , $n \geq p$ and $G = S_{n}$ or $G = A_{n}$ (symmetric or alternating group) there exists a Galois extension $K / F_{q} (T)$ ramif…

math.NT2021

Local Statistics for Zeros of Artin-Schreier L-functions

Alexei Entin, Noam Pirani

We study the local statistics of zeros of $L$ -functions attached to Artin-Scheier curves over finite fields. We consider three families of Artin-Schreier $L$ -functions: the ordinar…