5 problems

Let $p$ be a prime, and let a reflective lattice of prime level mean a reflective lattice whose level is $p$. Prime-level conjecture. There is no reflective lattice of prime level…

Let $T$ be a lattice with two negative squares, and let $\Delta$ be a primitive root system of $T$. For a primitive isotropic vector $c\in T$, write $S=c^\perp_T/[c]$ and denote by…

A Lie reflective automorphic form is an automorphic form having Fourier expansions of Lie type at all cusps, where a Fourier expansion of Lie type has integral Fourier coefficients…

Let $L$ be a lattice and consider $2U\oplus L(-1)$. Assume that $2U\oplus L(-1)$ has a modular form with complete $2$-divisor and that $L$ has no $2$-root. Complete 2-divisor conje…

Let $L$ be a positive-definite lattice such that $2U\oplus L(-1)$ is a $2$-reflective lattice of type (b), meaning that every lattice in the genus of $L$ has no $2$-root. Leech-lat…