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arXiv · 2111.10999

Conway invariant Jacobi forms on the Leech lattice

Kaiwen Sun·Haowu Wang
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Abstract

In this paper we study Jacobi forms associated with the Leech lattice $\Lambda$ which are invariant under the Conway group $\mathrm{Co}_0$. We determine and construct generators of modules of both weak and holomorphic Jacobi forms of integral weight and fixed index $t\leq 3$. As applications, (1) we find the modular linear differential equations satisfied by the holomorphic generators; (2) we determine the decomposition of many products of orbits of Leech vectors; (3) we calculate the intersection between orbits and Leech vectors; (4) we derive some conjugate relations among orbits modulo $t\Lambda$.

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Kaiwen Sun, Haowu Wang. 2021-11-22. Conway invariant Jacobi forms on the Leech lattice. https://arxiv.org/abs/2111.10999

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