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arXiv · 1401.0418

Mean Value Theorems for L-functions over Prime Polynomials for the Rational Function Field

Julio C. Andrade·Jonathan P. Keating
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Abstract

The first and second moments are established for the family of quadratic Dirichlet $L$--functions over the rational function field at the central point $s=\tfrac{1}{2}$ where the character $\chi$ is defined by the Legendre symbol for polynomials over finite fields and runs over all monic irreducible polynomials $P$ of a given odd degree. Asymptotic formulae are derived for fixed finite fields when the degree of $P$ is large. The first moment obtained here is the function field analogue of a result due to Jutila in the number--field setting. The approach is based on classical analytical methods and relies on the use of the analogue of the approximate functional equation for these $L$--functions.

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Julio C. Andrade, Jonathan P. Keating. 2014-01-02. Mean Value Theorems for L-functions over Prime Polynomials for the Rational Function Field. https://arxiv.org/abs/1401.0418

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