Asymptotic formula for the sum of a prime and a square-full number in short intervals
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917660109832192 |
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| author | Ogihara, Fumi Suzuki, Yuta |
| author_facet | Ogihara, Fumi Suzuki, Yuta |
| contents | Let $R_{m, \mathrm{sq-full}}(N)$ be a representation function for the sum of a prime and a square-full number. In this article, we prove an asymptotic formula for the sum of $R_{m, \mathrm{sq-full}}(N)$ over positive integers $N$ in a short interval ($X$, $X+H$] of length $H$ slightly bigger than $X^{\frac{1}{2}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic formula for the sum of a prime and a square-full number in short intervals Ogihara, Fumi Suzuki, Yuta Number Theory 11P32 Let $R_{m, \mathrm{sq-full}}(N)$ be a representation function for the sum of a prime and a square-full number. In this article, we prove an asymptotic formula for the sum of $R_{m, \mathrm{sq-full}}(N)$ over positive integers $N$ in a short interval ($X$, $X+H$] of length $H$ slightly bigger than $X^{\frac{1}{2}}$. |
| title | Asymptotic formula for the sum of a prime and a square-full number in short intervals |
| topic | Number Theory 11P32 |
| url | https://arxiv.org/abs/2405.04509 |