Eigenfunctions of the Fourier Transform with specified zeros
Metric Geometry
2023-06-22 v3 Classical Analysis and ODEs
Number Theory
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.
Cite
@article{arxiv.1907.08558,
title = {Eigenfunctions of the Fourier Transform with specified zeros},
author = {Ahram S. Feigenbaum and Peter J. Grabner and Douglas P. Hardin},
journal= {arXiv preprint arXiv:1907.08558},
year = {2023}
}