Hybrid Euler-Hadamard Product for Dirichlet $L$-functions with Prime conductors over Function Fields

Abstract

In this paper we extend the hybrid Euler-Hadamard product model for quadratic Dirichlet $L$-functions associated to irreducible polynomials over function fields. We also establish an asymptotic formula for the first twisted moment in this family of L-functions and then we provide further evidence for the conjectural asymptotic formulas for its moments.

arXiv comment20 pages, comments are welcome

References in corpus (5)

• The Mean Value of $L(\frac{1}{2},\chi )$ in the Hyperelliptic Ensemble
• Conjectures for the integral moments and ratios of L-functions over function fields
• The first moment of quadratic Dirichlet L-functions
• Truncated Product Representations for $L$-Functions in the Hyperelliptic Ensemble
• The fourth moment of quadratic Dirichlet $L$-functions