TL;DR
This paper explores how Viazovska's groundbreaking solution to the 8D sphere packing problem, which uses modular forms, has inspired new Fourier interpolation theorems, demonstrating the deep connections between geometry and analysis.
Contribution
It introduces new Fourier interpolation theorems derived from Viazovska's sphere packing methods, bridging geometric packing solutions and Fourier analysis.
Findings
New Fourier interpolation theorems established
Connections between sphere packing and Fourier analysis demonstrated
Mathematical techniques involving modular forms applied to interpolation
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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