10 problems

Let $\Gamma=SL_2(\mathbb Z)$, let $G_s(z_1,z_2)$ be the Green's function, and let … For a weakly holomorphic modular form $f=\sum_m c_f(m)q^m$ of weight $-2j$, define … For a discr…

Let $Z(W_\mathbb{Q})$ be the CM cycle and let $\Phi^r_L(z,h,f)$ be the higher Green function in the setting of Theorem. Assume that $f$ has integral Fourier coefficients and that t…

Let $(G,X,\Gamma)$ be a real Shimura datum and let $W\subset S_\Gamma$ be an irreducible algebraic subvariety. A CM-point is a point of $S_\Gamma$ at which the Mumford–Tate group o…

For a rational two-dimensional subspace $L$ of $\mathbb{R}^4$, let its discriminant be $\operatorname{disc}(L)=\operatorname{vol}(L/(L\cap\mathbb{Z}^4))^2$, and let $\mathcal{R}_D$…

Let $Y\subset {\rm Sh}_K^0({\mathbf P},X)$ be a closed irreducible algebraic subvariety of a connected mixed Shimura variety. Classical André–Oort conjecture. If $Y$ contains a Zar…

Equidistribution conjecture. Under the stated finiteness condition, the Galois-orbit measures $\mu_i$ converge weak-$*$ to the uniform probability measure on $X$.

Let $k\in\mathbb{N}_{>1}$ and $N\in\mathbb{N}$. Let $\mathcal G_k$ be the higher Green's function on $\mathbb{H}\times\mathbb{H}$ for $\Gamma_0(N)$, and suppose that the space of c…

Let $N\in\\{1,2,3,4\\}$, and let $z,z'\in\mathfrak H$ be quadratic irrational points satisfying … Assume that $z\notin\varGamma_0(N)z'$, where $\varGamma_0(N)$ is the Hecke congrue…

Let $k>1$ and let $\bm{\lambda}=\{\lambda_m\}_{m=1}^{\infty}\in\bigoplus_{m=1}^{\infty}\mathbb{Z}$ be a relation for $S_{2k}(\operatorname{SL}_2(\mathbb{Z}))$, meaning that…

Let $A_{g,1}$ be the moduli space of principally polarized complex Abelian varieties of dimension $g$. Let $x$ be a CM point in $A_{g,1}$ corresponding to a principally polarized A…