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arXiv · 2303.13427

On Viazovska's modular form inequalities

Dan Romik
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Abstract

Viazovska proved that the $E_8$ lattice sphere packing is the densest sphere packing in 8 dimensions. Her proof relies on two inequalities between functions defined in terms of modular and quasimodular forms. We give a direct proof of these inequalities that does not rely on computer calculations.

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Dan Romik. 2023-03-23. On Viazovska's modular form inequalities. https://arxiv.org/abs/2303.13427

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