Moments of traces of random symplectic matrices and hyperelliptic $L$-functions

Alexei Entin, Noam Pirani

We study matrix integrals of the form $${\int }_{\mathrm{USp}(2n)}\prod _{j=1}^k\mathrm{tr}(U^j{)}^{a_j}\mathrm{d}U,$$ where $a_1,\dots ,a_r$ are natural numbers and integration is with…