### 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.

Original language | English |
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Number of pages | 43 |

Journal | Mathematical Proceedings of the Cambridge Philosophical Society |

Publication status | Accepted/In press - 2020 |

### Fields of Expertise

- Information, Communication & Computing

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## Cite this

Feigenbaum, A., Grabner, P., & Hardin, D. (Accepted/In press). Eigenfunctions of the Fourier Transform with specified zeros.

*Mathematical Proceedings of the Cambridge Philosophical Society*.