Eigenfunctions of the Fourier Transform with specified zeros

Abstract

We give a unified description of the modular and quasi-modular functions used in Viazovska's proof of the best packing bounds in dimension 8 and the proof by Cohn, Kumar, Miller, Radchenko, and Viazovska of the best packing bound in dimension 24. We show that necessarily modular forms have to be used to obtain these results. We extend these constructions to arbitrary dimensions divisible by 4.

References in corpus (5)

• The sphere packing problem in dimension 24
• The sphere packing problem in dimension 8
• A conceptual breakthrough in sphere packing
• Fourier interpolation on the real line
• A Breakthrough in Sphere Packing: The Search for Magic Functions

Cited by in corpus (1)

• Sphere Packings in Euclidean Space with Forbidden Distances