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Six-dimensional sphere packing and linear programming

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arxiv 2211.09044 v4 pith:OBBBKI6M submitted 2022-11-16 math.MG math.NT

Matthew de Courcy-Ireland , Maria Dostert , Maryna Viazovska This is my paper · ORCID
classification math.MGmath.NT
keywords linearpackingprogrammingsphereboundcasecharactercohn-elkies
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We prove that the Cohn-Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn-Triantafillou to the case of odd weight and non-trivial character.

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  1. A dual linear programming bound for sphere packing in dimension 36

    math.MG 2026-07 conditional novelty 6.0 of 10

    In dimension 36, a modular-form certificate proves the Cohn–Elkies LP bound exceeds the density of the best known packing by at least a factor of 32.9.

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