Hybrid Euler-Hadamard product for quadratic Dirichlet $L$-functions in function fields

Abstract

We develop a hybrid Euler-Hadamard product model for quadratic Dirichlet $L$--functions over function fields (following the model introduced by Gonek, Hughes and Keating for the Riemann-zeta function). After computing the first three twisted moments in this family of $L$--functions, we provide further evidence for the conjectural asymptotic formulas for the moments of the family.

References in corpus (3)

• 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
• Truncated Product Representations for $L$-Functions in the Hyperelliptic Ensemble

Cited by in corpus (2)

• Complex Moments and the distribution of Values of $L(1,{\chi }_D)$ over Function Fields with Applications to Class Numbers
• Moments of quadratic Dirichlet $L$-functions over Function Fields