Moments with prime conductor in the function-field quadratic family

Establish the conjectured asymptotic formulas for all integral moments of the central values L(1/2,χ_P) averaged over monic irreducible polynomials P of degree 2g+1 over F_q[t].

Background

The paper discusses the function-field analogue in which quadratic characters are indexed by monic irreducible polynomials of degree 2g+1. Known first- and second-moment asymptotics are summarized, including an improved second-moment formula and later conjectures for general integral moments.

The cited conjecture is presented as an adaptation of the Conrey–Farmer–Keating–Rubinstein–Snaith heuristic to the prime-conductor function-field family. The paper proves a mixed second-moment result involving the second derivative of the completed L-function, but it does not establish the full collection of integral moment asymptotics.