$2$-reflective lattices of signature $(n,2)$ with $n\geq 8$

Autor:	Wang, Haowu
Rok vydání:	2023
Předmět:	Mathematics - Number Theory Mathematics - Algebraic Geometry 11F55 51F15 17B67 14J28
Druh dokumentu:	Working Paper
Popis:	An even lattice $M$ of signature $(n,2)$ is called $2$-reflective if there is a non-constant modular form for the orthogonal group of $M$ which vanishes only on quadratic divisors orthogonal to $2$-roots of $M$. In [Amer. J. Math. 2017] Shouhei Ma proved that there are only finitely many $2$-reflective lattices of signature $(n,2)$ with $n\geq 7$. In this paper we extend the finiteness result of Ma to $n\geq 5$ and show that there are exactly forty-two $2$-reflective lattices of signature $(n,2)$ with $n\geq 8$. Comment: 12 pages, comments welcome!
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.11536 Zobrazit plný text záznamu View this record from Arxiv