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Mergelyan's theorem with zero-free polynomials
Decide whether functions holomorphic and zero-free inside a compact set can be uniformly approximated by polynomials with no zeros on the set.
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "analysis", |
| 5 | "number-theory" |
| 6 | ], |
| 7 | "type": "proof", |
| 8 | "source": { |
| 9 | "key": "aimpl", |
| 10 | "name": "AIM Problem Lists", |
| 11 | "url": "http://aimpl.org/hyperbolicpoly/9/", |
| 12 | "id": "hyperbolicpoly 9.1", |
| 13 | "curator": "American Institute of Mathematics", |
| 14 | "poser": "Paul Gauthier", |
| 15 | "status": "open", |
| 16 | "as_of": "2026-10-20", |
| 17 | "catalog": "0521c19bbd38" |
| 18 | } |
| 19 | } |