4 problems

The characterization of Eisenstein-type forms. The subspace of $M_{a,b}(\operatorname{SO}(\Lambda),\vartheta_d)$ spanned by forms of Eisenstein type is the span of constant functio…

Let $G_p$ be the genus of lattices of rank $6$ and discriminant $D=p$. Kernel-dimension conjecture. The kernel of $\theta^{(2)}$ on $G_p$ has dimension equal to the number of class…

Let $G_p$ be the genus of lattices of rank $6$ and discriminant $p$, and let $k_p$ be the number of isomorphism classes in $G_p$ of lattices with no automorphism of determinant…

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…