7 problems

Let $F$ be the real quadratic field and let $K$ be a CM extension of $F$ as in the preceding construction. Write $\mathcal{O}_F$ for the ring of integers of $F$, let $\mathfrak l$…

Cheng–Duncan conjecture. For each conjugacy class $g$ of $M_{24}$, the product $\Phi_g$ defines a Siegel modular form with some multiplier on the congruence subgroup…

Let $\Theta_f$ be a theta block of $q$-order one that is a holomorphic Jacobi form of integral weight $k$ and integral index $N$ for $A_1$. Let $\operatorname{Grit}(\Theta_f)$ deno…

Let $d$ be the discriminant parameter of the imaginary quadratic field underlying the unitary group, let $L$ be a Hermitian lattice of signature $(n,1)$, and let…

Let the pure theta block $\Theta_f$ be a holomorphic Jacobi form of weight $k$ and index $m$ with vanishing order $1$ in $q$, where $k,m\in\mathbb Z_{>0}$. Define the nearly holomo…

Let $F$ be a Borcherds product of singular weight for an even lattice $M$ of signature $(2,n)$ with $n\geq 3$. Singular-weight Borcherds products conjecture. There exists an even l…

Let $L$ be the lattice indexing the Jacobi-form space $J_{k,L,1}$, and let $\phi\in J_{k,L,1}$. Let $T_{-}(2)$ denote the index-raising Hecke operator, and let…