Six-dimensional sphere packing and linear programming

de Courcy-Ireland, Matthew; Dostert, Maria; Viazovska, Maryna

doi:10.1090/mcom/3959

Six-dimensional sphere packing and linear programming
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by Matthew de Courcy-Ireland, Maria Dostert and Maryna Viazovska;

Math. Comp. 93 (2024), 1993-2029

DOI: https://doi.org/10.1090/mcom/3959

Published electronically: March 20, 2024

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Previous version: Original version posted March 20, 2024
Corrected version: This paper has been republished to rectify an omission in the bibliographic information.

Abstract:

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 [Math. Comp. 91 (2021), pp. 491–508] to the case of odd weight and non-trivial character.

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