On the non-existence of singular Borcherds products
| Autor: | Wang, Haowu, Williams, Brandon |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $l\geq 3$ and $F$ be a modular form of weight $l/2-1$ on $\mathrm{O}(l,2)$ which vanishes only on rational quadratic divisors. We prove that $F$ has only simple zeros and that $F$ is anti-invariant under every reflection fixing a quadratic divisor in the zeros of $F$. In particular, $F$ is a reflective modular form. As a corollary, the existence of $F$ leads to $l\leq 20$ or $l=26$, in which case $F$ equals the Borcherds form on $\mathrm{II}_{26,2}$. This answers a question posed by Borcherds in 1995. Comment: 7 pages, this paper is an extension of Section 3 of arXiv:2207.14518 v1, which will be removed in the new version. Comments welcome! |
| Databáze: | arXiv |
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