Eigenfunctions of the Fourier Transform with specified zeros

Ahram Feigenbaum, Peter Grabner, Douglas Hardin

Publikation: Beitrag in einer FachzeitschriftArtikel

Abstract

Eigenfunctions of the Fourier transform with prescribed zeros played a major role in the proof that the E8 and the Leech lattice give the best sphere packings in respective dimensions 8 and 24 by Cohn, Kumar, Miller, Radchenko and Viazovska. The functions used for a linear programming argument were constructed as Laplace transforms of certain modular and quasimodular forms. Similar constructions were used by Cohn and Gonçalves to find a function satisfying an optimal uncertainty principle in dimension 12. This paper gives a unified view on these constructions and develops the machinery to find the underlying forms in all dimensions divisible by 4. Furthermore, the positivity of the Fourier coefficients of the quasimodular forms occurring in this context is discussed.
Originalspracheenglisch
Seiten (von - bis)329-367
Seitenumfang39
FachzeitschriftMathematical Proceedings of the Cambridge Philosophical Society
Jahrgang171
Ausgabenummer2
Frühes Online-Datum15 Feb 2021
DOIs
PublikationsstatusVeröffentlicht - Sep 2021

ASJC Scopus subject areas

  • !!Mathematics(all)

Fields of Expertise

  • Information, Communication & Computing

Fingerprint

Untersuchen Sie die Forschungsthemen von „Eigenfunctions of the Fourier Transform with specified zeros“. Zusammen bilden sie einen einzigartigen Fingerprint.

Dieses zitieren