6 problems

Let $n_1,n_2$ be non-negative integers, let $c(n_1,n_2)$ denote the leading-order coefficient in the mixed second-moment asymptotic for the relevant family of quadratic Dirichlet…

Let $d53d_d(d70e_1,d70e_2)$ be the number of real zeros of $L'(s,\chi_d)$ on the interval $[d70e_1,d70e_2]$, where $\chi_d$ is the primitive quadratic character attached to the fun…

Let $k_1,k_2,n_1,n_2$ be non-negative integers, put $k=k_1+k_2$, and let $\mathcal{P}_{2g+1}$ denote the set of monic irreducible polynomials of degree $2g+1$ over…

The first moment in question is the family of quadratic Dirichlet $L$-functions studied by Goldfeld and Hoffstein, with summation parameter $X$. Goldfeld–Hoffstein conjecture. The…

Let $D_\pm(X)=\{d\in D(X):d\gtrless0\}$, and let $\mathcal Q_\pm(3,\log X)$ be the cubic-moment polynomials for the two signs. Zhang's conjecture. There are constants $b_+$ and…

Let $D_+(X)=\{d\in D(X):d>0\}$ and $D_-(X)=\{d\in D(X):d<0\}$, where $D(X)$ is the set of fundamental discriminants with $|d|<X$. For a positive integer $k$, let…