The integrated fourth moment of Dirichlet \(L\)-functions over rational function fields
The moments for families of \(L\)- functions is one of central problems. In the paper, hybrid (in both \(q\)- and \(t\)-aspect) fourth moment of Dirichlet \(L\)-functions over rational function fields \({\mathbb{F}}_q[t]\) are studied. This moment over primitive Dirichlet characters modulo polynomial \(Q\) and then over the whole critical circle (corresponding to the critical line in number field setting) is investigated. An asymptotic formula (with the leading four terms) for any monic polynomial and exact moment formula for irreducible monic polynomial, respectively, are given. As corollary, the shifted fourth moments are obtained.
scientific article; zbMATH DE number 7257233
scientific article