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Asmaa Shamesaldeen

Publications and source records attributed to Asmaa Shamesaldeen.

4 recordsLinked to original sources
arXiv2026

Correlations of zeros of a family of $L$-functions in function fields with symplectic symmetry

In this paper, we adapt the framework developed by Mason and Snaith to investigate the $n$-level density of zeros in the context of function fields. Specifically, we derive explicit formulas for the $n$-level density of zeros in families of quadratic Dirichlet $L$-functions associated with hyperelliptic curves of genus $g$ over the finite field $\mathbb{F}_{q}$. Employing Mason and Snaith's method, we obtain precise expressions for the $1$-level density in these families and extend the approach to higher-level densities. Furthermore, we apply the method to derive formulas for the $n$-level density of zeros in families of $L$-functions associated with prime characters. Our results are consistent with the findings of Andrade, Jung, and Shamesaldeen in the case $n=1$.

math.NT↗
arXiv2020

The Moments and statistical Distribution of Class number of Primes over Function Fields

We investigate the moment and the distribution of $L(1,\x_P),$ where $\x_P$ varies over quadratic characters associated to irreducible polynomials $P$ of degree $2g+1$ over $\mathbb{F}_q[T]$ as $g\to\infty$. In the first part of the paper we compute the integral moments of the class number $h_{P}$ associated to quadratic function fields with prime discriminants $P$ and this is done by adapting to the function field setting some of the previous results carried out by Nagoshi in the number field setting. In the second part of the paper we compute the complex moments of of $L(1,\x_P)$ in large uniform range and investigate the statistical distribution of the class numbers by introducing a certain random Euler product. The second part of the paper is based on recent results carried out by Lumley when dealing with square-free polynomials.

math.NT↗
arXiv2018

The Integral Moments and Ratios of Quadratic Dirichlet $L$-Functions over Monic Irreducible Polynomials in $\mathbb{F}_{q}[T]$

In this paper we extend to the function field setting the heuristics formerly developed by Conrey, Farmer, Keating, Rubinstein and Snaith, for the integral moments of $L$-functions. We also adapt to the function setting the heuristics first developed by Conrey, Farmer and Zirnbauer to the study of mean values of ratios of $L$-functions. Specifically, the focus of this paper is on the family of quadratic Dirichlet $L$-functions $L(s,χ_{P})$ where the character $χ$ is defined by the Legendre symbol for polynomials in $\mathbb{F}_{q}[T]$ with $\mathbb{F}_{q}$ a finite field of odd cardinality and the averages are taken over all monic and irreducible polynomials $P$ of a given odd degree. As an application we also compute the formula for the one-level density for the zeros of these $L$-functions.

math.NT↗