{"paper":{"title":"Hermite polynomials, linear flows on the torus, and an uncertainty principle for roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Diogo Oliveira e Silva, Felipe Gon\\c{c}alves, Stefan Steinerberger","submitted_at":"2016-02-10T13:29:41Z","abstract_excerpt":"We study a recent result of Bourgain, Clozel and Kahane, a version of which states that a sufficiently nice function $f:\\mathbb{R} \\rightarrow \\mathbb{R}$ that coincides with its Fourier transform and vanishes at the origin has a root in the interval $(c, \\infty)$, where the optimal $c$ satisfies $0.41 \\leq c \\leq 0.64$. A similar result holds in higher dimensions. We improve the one-dimensional result to $0.45 \\leq c \\leq 0.594$, and the lower bound in higher dimensions. We also prove that extremizers exist, and have infinitely many double roots. With this purpose in mind, we establish a new "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.03366","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}