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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2410.10856 |
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| _version_ | 1866915072239992832 |
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| author | Guria, Rachita |
| author_facet | Guria, Rachita |
| contents | We obtain an asymptotic formula with a power-saving error term for counting the integer points $(a,b,c,d)$ in an expanding box $[-X,X]^4$ that satisfy the determinant equation $x_1x_2-x_3x_4=r$ for $r \neq 0$ with two of entries to be prime. The method involves the Poisson summation formula and the estimation for the average of the sums of the Kloosterman fractions over primes $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10856 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An asymptotic formula with power-saving error term for counting prime solutions to a binary additive problem Guria, Rachita Number Theory Primary 11P21, 11P05, 11L07, 11L20, Secondary 11N36, 11C20, 11D09 We obtain an asymptotic formula with a power-saving error term for counting the integer points $(a,b,c,d)$ in an expanding box $[-X,X]^4$ that satisfy the determinant equation $x_1x_2-x_3x_4=r$ for $r \neq 0$ with two of entries to be prime. The method involves the Poisson summation formula and the estimation for the average of the sums of the Kloosterman fractions over primes $p$. |
| title | An asymptotic formula with power-saving error term for counting prime solutions to a binary additive problem |
| topic | Number Theory Primary 11P21, 11P05, 11L07, 11L20, Secondary 11N36, 11C20, 11D09 |
| url | https://arxiv.org/abs/2410.10856 |