On Viazovska's modular form inequalities

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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Bibliographic Details
Main Author:	Romik, Dan
Format:	Journal Article
Language:	English
Published:	23-03-2023
Subjects:	Mathematics - Metric Geometry Mathematics - Number Theory
Online Access:	Get full text
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Description
Summary:	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.
DOI:	10.48550/arxiv.2303.13427