8 problems

Finite-field counting conjecture. The number of solutions of this system over $\mathbb F_{p^n}$ is an alternating sum of exponentials in $n$, with the total number of terms bounded…

Fix an integer $n\geqslant 2$, and let $F_n(X)$ denote the number of degree-$n$ number fields $K$ with $|\Delta_K|\leqslant X$. The discriminant of $K$ is denoted by $\Delta_K$. Fo…

Let $d$ be a positive integer, let $X$ tend to infinity, and count weight $2$ newforms of degree $d$ and squarefree level $N\leq X$, up to the counting convention used in the paper…

For $2\leq m\leq5$, let $\mathcal{Z}_{1,m,\mathbb{Q}}(\mathcal{B})$ count $m$-marked $(m-1)$-stable genus-one curves over $\mathbb{Z}$ ordered by…

Let $\mathcal{Z}_{1,\mathbb{Q}}^{[\Gamma]}(\mathcal{B})$ count generalized elliptic curves with $[\Gamma]$-structures over $\mathbb{Z}$ ordered by…

For $g\geq3$, let $\mathcal{Z}_{g,\mathbb{Q}}(\mathcal{B})$ count stable hyperelliptic genus $g$ curves with a marked rational Weierstrass point over $\mathbb{Z}$ satisfying…

Let $\mathcal{N}_{2,\mathbb{Q}}(\mathcal{B})$ count principally polarized abelian surfaces $A=\operatorname{Jac}(X)$, where $X$ is a stable genus $2$ curve over $\mathbb{Z}$ satisf…

Let $K/{\mathbb Q}$ be a number field of degree $d$. Let $N_d(B)$ denote the counting function from Theorem, and let $\alpha_K$ be the associated exponent. Degree-dependence conjec…