Eigenfunctions of the Fourier Transform with specified zeros

Ahram Feigenbaum, Peter Grabner, Douglas Hardin

Research output: Contribution to journalArticle


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 languageEnglish
Number of pages43
JournalMathematical Proceedings of the Cambridge Philosophical Society
Publication statusAccepted/In press - 2020

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