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- Title
Sign uncertainty principles and low-degree polynomials.
- Authors
Cohn, Henry; Dong, Dingding; Gonçalves, Felipe
- Abstract
We prove an asymptotically sharp version of the Bourgain–Clozel–Kahane and Cohn–Gonçalves sign uncertainty principles for polynomials of sublinear degree times a Gaussian, as the dimension tends to infinity. In particular, we show that polynomials whose degree is sublinear in the dimension cannot improve asymptotically on those of degree at most three. This question arises naturally in the study of both linear programming bounds for sphere packing and the spinless modular bootstrap bound for free bosons.
- Subjects
HEISENBERG uncertainty principle; POLYNOMIALS; LINEAR programming; BOSONS; SPHERE packings
- Publication
Proceedings of the American Mathematical Society, Series B, 2024, Vol 11, p224
- ISSN
2330-1511
- Publication type
Article
- DOI
10.1090/bproc/219