On the third moment of $L(\frac{1}{2},{\chi }_d)$ I: the rational function field case

Abstract

In this note, we prove the existence of a secondary term in the asymptotic formula of the cubic moment of quadratic Dirichlet L-functions $$\sum _{\begin{array}{c}d-\mathrm{monic}\&sq.\mathrm{free}\mathrm{deg}d=D\end{array}}L(\frac{1}{2},{\chi }_d{)}^3$$ over rational function fields on the order of $q^{\frac{3}{4}D}.$ This term is in perfect analogy with the $x^{\frac{3}{4}}$-term indicated in our joint work arXiv:math/0110092v1 for the corresponding asymptotic formula over the rationals.

29 pages

Cited by in corpus (2)

• Moments of quadratic twists of elliptic curve L-functions over function fields
• A representation theory approach to integral moments of L-functions over function fields