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On Viazovskas modular form inequalities.
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https://doi.org/10.1073/pnas.2304891120Abstract
Viazovska proved that the [Formula: see text] lattice sphere packing is the densest sphere packing in [Formula: see text] 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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