Asif Zaman

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20242026

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6 papers · 1 filter

math.NT2026

Numerical computations concerning Landau-Siegel zeros

Rick F. Lu, Asif Zaman, Haonan Zhao

We computationally verify that if $L (s, χ)$ is a quadratic Dirichlet $L$ -function modulo $q \leq 1 0^{10}$ then $L (σ, χ) \neq = 0$ for real $σ \geq 1 - 1/ (5 lo g q)$ . The number of verified…

math.NT2025

The least prime with a given cycle type

Peter J. Cho, Robert J. Lemke Oliver, Asif Zaman

Let $G$ be a finite group. Let $K / k$ be a Galois extension of number fields with Galois group isomorphic to $G$ , and let $C \subseteq Gal (K / k) ≃ G$ be a conjugacy inv…

math.NT2025

Central limit theorems for random multiplicative functions over function fields

Declan Hoban, Jibran Iqbal Shah, Nadya-Catherine Ismail +2

We provide a sufficient characterization for subsets $A$ of the polynomial ring $F_{q} [t]$ for which partial sums of Steinhaus random multiplicative functions appr…

math.NT2025

Effective Brauer-Siegel theorems for Artin $L$ -functions

Peter J. Cho, Robert J. Lemke Oliver, Asif Zaman

Given a number field $K \neq = Q$ , in a now classic work, Stark pinpointed the possible source of a so-called Landau-Siegel zero of the Dedekind zeta function $ζ_{K} (s)$ and u…

math.NT2025

Improving the trivial bound for $ℓ$ -torsion in class groups

Robert J. Lemke Oliver, Asif Zaman

For any number field $K$ with $D_{K} = ∣ Disc (K) ∣$ and any integer $ℓ \geq 2$ , we improve over the commonly cited trivial bound $|\mathrm{Cl}_K[\ell]| \leq |\mathrm{Cl}_K| \…

math.NT2024

Explicit Deuring-Heilbronn phenomenon for Dirichlet $L$ -functions

Kübra Benli, Shivani Goel, Henry Twiss +1

Assuming the existence of a Landau-Siegel zero, we establish an explicit Deuring-Heilbronn zero repulsion phenomenon for Dirichlet $L$ -functions modulo $q$ . Our estimate is uniform…

Numerical computations concerning Landau-Siegel zeros

The least prime with a given cycle type

Central limit theorems for random multiplicative functions over function fields

Effective Brauer-Siegel theorems for Artin L-functions

Improving the trivial bound for ℓ-torsion in class groups

Explicit Deuring-Heilbronn phenomenon for Dirichlet L-functions

Effective Brauer-Siegel theorems for Artin $L$ -functions

Improving the trivial bound for $ℓ$ -torsion in class groups

Explicit Deuring-Heilbronn phenomenon for Dirichlet $L$ -functions