Reflective Modular Forms: A Jacobi Forms Approach

DOI10.1093/IMRN/RNZ070zbMATH Open1487.11041arXiv1801.09590OpenAlexW2962677209MaRDI QIDQ5005261

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Publication date: 9 August 2021

Published in: (Search for Journal in Brave)

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 $ngeq15$ and $neq19$ 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 $2Uoplus2E_8(-1)opluslangle-2nangle$ 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.

Full work available at URL: https://arxiv.org/abs/1801.09590

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