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Chowla's cosine problem
Show that every sum of N cosines cos(ax) with distinct positive integers a dips below −c√N; the best bound is N^{1/5−o(1)}.
| 1 | { |
| 2 | "domain": "mathematics", |
| 3 | "topics": [ |
| 4 | "analysis", |
| 5 | "number-theory" |
| 6 | ], |
| 7 | "type": "proof", |
| 8 | "source": { |
| 9 | "key": "erdos", |
| 10 | "name": "Erdős Problems", |
| 11 | "url": "https://www.erdosproblems.com/510", |
| 12 | "id": "510", |
| 13 | "curator": "Thomas Bloom", |
| 14 | "poser": "Sarvadaman Chowla", |
| 15 | "status": "open", |
| 16 | "as_of": "2026-10-20", |
| 17 | "catalog": "0521c19bbd38" |
| 18 | }, |
| 19 | "review": true, |
| 20 | "approval": "first-time" |
| 21 | } |