4 problems

Let $k\geqslant 4$ and consider moments of quadratic Dirichlet $L$-functions over fundamental discriminants, such as smoothed sums of $L(1/2,\chi_d)^k$ over positive discriminants…

Let $E_1(X)$ be the error term in the asymptotic formula for the first moment of quadratic Dirichlet $L$-functions, … where $P_1$ is an explicit polynomial and the sum is over fund…

Let $q$ be fixed, let $\mathcal{H}_{2g+1}$ be the set of monic square-free polynomials of degree $2g+1$ over $\mathbb{F}_q[x]$, and define … For $k\in\mathbb{N}$, define … where…

Symplectic-family moment conjecture. For $k\in\mathbb{N}$,