Ahammad Mostafa Hossain

Preprint Sep 2026

Extreme Values of Quadratic Dirichlet $L$-functions over Monic Irreducible Polynomials in $\mathbb{F}_q[t]$

In this paper, we establish a new $\Omega$-result for the values $|L(\sigma,\chi_P)|$ of quadratic Dirichlet $L$-functions at and near the central point, where \[ \sigma=\frac12+\frac{\kappa}{\ln g}, \qquad \kappa\geq 0, \] and $P$ ranges over monic irreducible polynomials associated with hyperelliptic curves of genus...

Ahammad Mostafa Hossain · 1 citation

Preprint Sep 2026

Extreme Values of Quadratic Dirichlet $L$-functions over Monic Irreducible Polynomials in $\mathbb{F}_q[t]$

In this paper, we establish a new $\Omega$-result for the central values $|L(1/2,\chi_P)|$ of quadratic Dirichlet $L$-functions, where $P$ ranges over monic irreducible polynomials associated with hyperelliptic curves of genus $g$ over a fixed finite field $\mathbb{F}_q$. We consider the asymptotic setting in which $q$...

Ahammad Mostafa Hossain · 1 citation

Preprint Sep 2026

Extreme Values of Quadratic Dirichlet $L$-Functions over Monic Irreducible Polynomials in $\mathbb{F}_q[t]$

In this paper, we establish a new $\Omega$-result for the central values $|L(1/2,\chi_P)|$ of quadratic Dirichlet $L$-functions, where $P$ ranges over monic irreducible polynomials associated with hyperelliptic curves of genus $g$ over a fixed finite field $\mathbb{F}_q$. We consider the asymptotic setting in which $q$...

Ahammad Mostafa Hossain · 1 citation