3 problems

Let $M$ be an even lattice of signature $(n,2)$ with $n\geq 3$. A modular form on a finite-index subgroup of $\mathop{\mathrm O}\nolimits^+(M)$ is $2$-reflective if its zero diviso…

Let $M$ be an even lattice of signature $(n,2)$ with $n\geq 3$. Let $\mathcal D(M)$ be the associated type IV Hermitian symmetric domain, and call a non-constant modular form on a…

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…