Sign uncertainty principles and low-degree polynomials
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917714131419136 |
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| author | Cohn, Henry Dong, Dingding Gonçalves, Felipe |
| author_facet | Cohn, Henry Dong, Dingding Gonçalves, Felipe |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01684 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sign uncertainty principles and low-degree polynomials Cohn, Henry Dong, Dingding Gonçalves, Felipe Classical Analysis and ODEs 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. |
| title | Sign uncertainty principles and low-degree polynomials |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2210.01684 |