{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/flat-littlewood-polynomials-exist","title":"Flat Littlewood Polynomials Exist","arxiv_id":"1907.09464","date":"2019-07-22","proceeding":null,"authors":["Paul Balister","Béla Bollobás","Robert Morris","Julian Sahasrabudhe","Marius Tiba"],"abstract":"We show that there exist absolute constants $\\Delta > \\delta > 0$ such that, for all $n \\geqslant 2$, there exists a polynomial $P$ of degree $n$, with $\\pm 1$ coefficients, such that $$\\delta\\sqrt{n} \\leqslant |P(z)| \\leqslant \\Delta\\sqrt{n}$$ for all $z\\in\\mathbb{C}$ with $|z|=1$. This confirms a conjecture of Littlewood from 1966.","url_abs":"http://arxiv.org/abs/1907.09464v1","url_pdf":"http://arxiv.org/pdf/1907.09464v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"flat-littlewood-polynomials-exist","repo_url":"https://github.com/weightan/rootsMapPython","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}