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Some properties of optimal functions for sphere packing in dimensions 8 and 24

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arxiv 1603.04759 v1 pith:SZ3I654R submitted 2016-03-15 math.MG

Henry Cohn , Stephen D. Miller This is my paper · ORCID
classification math.MG
keywords functionsconjectureconjecturespackingpropertiessomespheredimension
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We study some sequences of functions of one real variable and conjecture that they converge uniformly to functions with certain positivity and growth properties. Our conjectures imply a conjecture of Cohn and Elkies, which in turn implies the complete solution to the sphere packing problem in dimensions 8 and 24. We give numerical evidence for these conjectures as well as some arithmetic properties of the hypothetical limiting functions. The conjectures are of greatest interest in dimension 24, in light of Viazovska's recent solution to the Cohn-Elkies conjecture (and consequently the sphere packing problem) in dimension 8.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. The 196560 auxiliary-function conjecture for the Leech lattice

    math.NT 2026-08 accept novelty 8.0 of 10

    The paper proves the Cohn-Kumar 196560 auxiliary-function conjecture by showing that all functions g_C = a_2 - C b_2 with C above a finite threshold satisfy the required sign conditions and Poisson-summation identity.

  2. Pair correlation for Dedekind zeta functions of abelian extensions

    math.NT 2019-08 conditional novelty 6.0 of 10

    Assuming GRH, the authors prove new upper bounds on the total multiplicity of zeros and deduce that at least 45.85% of zeros of quadratic-field Dedekind zeta functions are distinct.

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