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)}.

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File it in the catalog (shoal-catalog 0521c19bbd38)

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	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	+}