The inverse Sieve problem in high dimensions
We show that if a big set of integer points S ⊆ [0, N] d, d > 1, occupies few residue classes mod p for many primes p, then it must essentially lie in the solution set of some polynomial equation of low degree. This answers a question of Helfgott and Venkatesh. © 2012.
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2012
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v161_n10_p2001_Walsh http://hdl.handle.net/20.500.12110/paper_00127094_v161_n10_p2001_Walsh |
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paper:paper_00127094_v161_n10_p2001_Walsh2023-06-08T14:35:26Z The inverse Sieve problem in high dimensions Walsh, Miguel Nicolás We show that if a big set of integer points S ⊆ [0, N] d, d > 1, occupies few residue classes mod p for many primes p, then it must essentially lie in the solution set of some polynomial equation of low degree. This answers a question of Helfgott and Venkatesh. © 2012. Fil:Walsh, M.N. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2012 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v161_n10_p2001_Walsh http://hdl.handle.net/20.500.12110/paper_00127094_v161_n10_p2001_Walsh |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
We show that if a big set of integer points S ⊆ [0, N] d, d > 1, occupies few residue classes mod p for many primes p, then it must essentially lie in the solution set of some polynomial equation of low degree. This answers a question of Helfgott and Venkatesh. © 2012. |
| author |
Walsh, Miguel Nicolás |
| spellingShingle |
Walsh, Miguel Nicolás The inverse Sieve problem in high dimensions |
| author_facet |
Walsh, Miguel Nicolás |
| author_sort |
Walsh, Miguel Nicolás |
| title |
The inverse Sieve problem in high dimensions |
| title_short |
The inverse Sieve problem in high dimensions |
| title_full |
The inverse Sieve problem in high dimensions |
| title_fullStr |
The inverse Sieve problem in high dimensions |
| title_full_unstemmed |
The inverse Sieve problem in high dimensions |
| title_sort |
inverse sieve problem in high dimensions |
| publishDate |
2012 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00127094_v161_n10_p2001_Walsh http://hdl.handle.net/20.500.12110/paper_00127094_v161_n10_p2001_Walsh |
| work_keys_str_mv |
AT walshmiguelnicolas theinversesieveprobleminhighdimensions AT walshmiguelnicolas inversesieveprobleminhighdimensions |
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1768543828217692160 |