From sphere packing to Fourier interpolation

Cohn, Henry

doi:10.1090/bull/1813

From sphere packing to Fourier interpolation
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by Henry Cohn;

Bull. Amer. Math. Soc. 61 (2024), 3-22

DOI: https://doi.org/10.1090/bull/1813

Published electronically: October 6, 2023

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Abstract:

Viazovska’s solution of the sphere packing problem in eight dimensions is based on a remarkable construction of certain special functions using modular forms. Great mathematics has consequences far beyond the problems that originally inspired it, and Viazovska’s work is no exception. In this article, we’ll examine how it has led to new interpolation theorems in Fourier analysis, specifically a theorem of Radchenko and Viazovska.

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