Alexandru Popa
Simion Stoilow Institute of Mathematics of the Romanian Academy

After reviewing recent progress in the moment problem, I will present an asymptotic formula for a "smoothed" fourth moment of quadratic Dirichlet $L$-functions over function fields, exhibiting infinitely many terms in the asymptotic expansion. The proof involves studying the multiple Dirichlet series associated with the fourth moment, a series in five complex variables satisfying an infinite group of functional equations. We show that this series can be analytically continued to an optimal domain, using a new type of functional equation. This is joint work with Adrian Diaconu and Vicenţiu Paşol.