Large sieve inequalities with power moduli and Waring's problem
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910661599035392 |
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| author | Baier, Stephan Lynch, Sean B. |
| author_facet | Baier, Stephan Lynch, Sean B. |
| contents | We improve the large sieve inequality with $k$th-power moduli, for all $k\ge 4$. Our method relates these inequalities to a restricted variant of Waring's problem. Firstly, we input a classical divisor bound on the number of representations of a positive integer as a sum of two $k$th-powers. Secondly, we input a recent and general result of Wooley on mean values of exponential sums. Lastly, we state a conditional result, based on the conjectural Hardy-Littlewood formula for the number of representations of a large positive integer as a sum of $k+1$ $k$th-powers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_07613 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Large sieve inequalities with power moduli and Waring's problem Baier, Stephan Lynch, Sean B. Number Theory 11B57, 11P05 (Primary) 11D75, 11J71, 11L03, 11L07 (Secondary) We improve the large sieve inequality with $k$th-power moduli, for all $k\ge 4$. Our method relates these inequalities to a restricted variant of Waring's problem. Firstly, we input a classical divisor bound on the number of representations of a positive integer as a sum of two $k$th-powers. Secondly, we input a recent and general result of Wooley on mean values of exponential sums. Lastly, we state a conditional result, based on the conjectural Hardy-Littlewood formula for the number of representations of a large positive integer as a sum of $k+1$ $k$th-powers. |
| title | Large sieve inequalities with power moduli and Waring's problem |
| topic | Number Theory 11B57, 11P05 (Primary) 11D75, 11J71, 11L03, 11L07 (Secondary) |
| url | https://arxiv.org/abs/2303.07613 |