The level of distribution of the sum-of-digits function in arithmetic progressions
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909563516616704 |
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| author | Toumi, Nathan |
| author_facet | Toumi, Nathan |
| contents | For $q \geq 2$, $n \in \mathbb{N}$, let $s_{q}(n)$ denote the sum of the digits of $n$ written in base $q$. Spiegelhofer (2020) proved that the Thue--Morse sequence has level of distribution $1$, improving on a former result of Fouvry and Mauduit (1996). In this paper we generalize this result to sequences of type $\left\{\exp\left(2πi\ell s_q(n)/b\right)\right\}_{n \in \mathbb{N}}$ and provide an explicit exponent in the upper bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02784 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The level of distribution of the sum-of-digits function in arithmetic progressions Toumi, Nathan Number Theory 11A05, 11A07, 11B25, 11B50, 11B57, 11B85, 11L07, 11N37, 11N64 For $q \geq 2$, $n \in \mathbb{N}$, let $s_{q}(n)$ denote the sum of the digits of $n$ written in base $q$. Spiegelhofer (2020) proved that the Thue--Morse sequence has level of distribution $1$, improving on a former result of Fouvry and Mauduit (1996). In this paper we generalize this result to sequences of type $\left\{\exp\left(2πi\ell s_q(n)/b\right)\right\}_{n \in \mathbb{N}}$ and provide an explicit exponent in the upper bound. |
| title | The level of distribution of the sum-of-digits function in arithmetic progressions |
| topic | Number Theory 11A05, 11A07, 11B25, 11B50, 11B57, 11B85, 11L07, 11N37, 11N64 |
| url | https://arxiv.org/abs/2504.02784 |