2023/01/27 by Haowu Wang, Wang, Haowu
Computer Science · Mathematics · #11F55 #14J28 #17B67 #51F15 #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2301.11536
openalex publication_date 2023/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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≥ 7. In this paper we extend the finiteness result of Ma to n≥ 5 and show that there are exactly forty-two 2-reflective lattices of signature (n,2) with n≥ 8.