Reflective modular forms: A Jacobi forms approach

2018/01/29 by Wang, Haowu
#11F50 #11F55 #14J28 #17B67 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1801.09590

Abstract

We give an explicit formula to express the weight of 2-reflective modular forms. We prove that there is no 2-reflective lattice of signature (2,n) when n≥ 15 and n≠ 19 except the even unimodular lattices of signature (2,18) and (2,26). As applications, we give a simple proof of Looijenga's theorem that the lattice 2U⊕ 2E₈(-1)⊕⟨ -2n⟩ is not 2-reflective if n>1. We also classify reflective modular forms on lattices of large rank and the modular forms with the simplest reflective divisors.

Related

• The classification of 2-reflective modular forms
• Finiteness of 2-reflective lattices of signature (2,n)
• 2-reflective lattices of signature (n,2) with n≥ 8
• On the classification of reflective modular forms
• Reflective modular forms on lattices of prime level