$2$-reflective lattices of signature $(n,2)$ with $n\geq 8$
Autor: | Wang, Haowu |
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Rok vydání: | 2023 |
Předmět: | |
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 |
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