Reflective modular forms: A Jacobi forms approach

Haowu Wang

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arXiv · 1801.09590

Reflective modular forms: A Jacobi forms approach

Haowu Wang

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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 $n\geq 15$ and $n\neq 19$ 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 $2U\oplus 2E_8(-1)\oplus\langle -2n\rangle$ 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.

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Haowu Wang. 2018-01-29. Reflective modular forms: A Jacobi forms approach. https://arxiv.org/abs/1801.09590

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