Flat Littlewood polynomials exist
We show that there exist absolute constants Δ>𝛿>0 such that, for all 𝑛≥2, there exists a polynomial 𝑃 of degree 𝑛, with coefficients in {−1,1}, such that 𝛿𝑛√≤|𝑃(𝑧)|≤Δ𝑛√ for all 𝑧∈ℂ with |𝑧|=1. This confirms a conjecture of Littlewood from 1966....
| Main Authors: | , , , , |
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| Format: | Journal article |
| Language: | English |
| Published: |
Mathematical Sciences Publishers
2020
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| _version_ | 1797085732069703680 |
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| author | Balister, P Bollobás, B Morris, R Sahasrabudhe, J Tiba, M |
| author_facet | Balister, P Bollobás, B Morris, R Sahasrabudhe, J Tiba, M |
| author_sort | Balister, P |
| collection | OXFORD |
| description | We show that there exist absolute constants Δ>𝛿>0 such that, for all 𝑛≥2, there exists a polynomial 𝑃 of degree 𝑛, with coefficients in {−1,1}, such that
𝛿𝑛√≤|𝑃(𝑧)|≤Δ𝑛√
for all 𝑧∈ℂ with |𝑧|=1. This confirms a conjecture of Littlewood from 1966. |
| first_indexed | 2024-03-07T02:12:07Z |
| format | Journal article |
| id | oxford-uuid:a101bce7-f2e3-4ce1-8e0e-42f646b8b0d5 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:12:07Z |
| publishDate | 2020 |
| publisher | Mathematical Sciences Publishers |
| record_format | dspace |
| spelling | oxford-uuid:a101bce7-f2e3-4ce1-8e0e-42f646b8b0d52022-03-27T02:09:55ZFlat Littlewood polynomials existJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a101bce7-f2e3-4ce1-8e0e-42f646b8b0d5EnglishSymplectic ElementsMathematical Sciences Publishers 2020Balister, PBollobás, BMorris, RSahasrabudhe, JTiba, MWe show that there exist absolute constants Δ>𝛿>0 such that, for all 𝑛≥2, there exists a polynomial 𝑃 of degree 𝑛, with coefficients in {−1,1}, such that 𝛿𝑛√≤|𝑃(𝑧)|≤Δ𝑛√ for all 𝑧∈ℂ with |𝑧|=1. This confirms a conjecture of Littlewood from 1966. |
| spellingShingle | Balister, P Bollobás, B Morris, R Sahasrabudhe, J Tiba, M Flat Littlewood polynomials exist |
| title | Flat Littlewood polynomials exist |
| title_full | Flat Littlewood polynomials exist |
| title_fullStr | Flat Littlewood polynomials exist |
| title_full_unstemmed | Flat Littlewood polynomials exist |
| title_short | Flat Littlewood polynomials exist |
| title_sort | flat littlewood polynomials exist |
| work_keys_str_mv | AT balisterp flatlittlewoodpolynomialsexist AT bollobasb flatlittlewoodpolynomialsexist AT morrisr flatlittlewoodpolynomialsexist AT sahasrabudhej flatlittlewoodpolynomialsexist AT tibam flatlittlewoodpolynomialsexist |