Mixed incomplete character sums of rational functions with smooth moduli
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909992068579328 |
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| author | Cochrane, Todd Granville, Andrew Zheng, Junren |
| author_facet | Cochrane, Todd Granville, Andrew Zheng, Junren |
| contents | Let $χ=χ_q$ be a primitive character mod $q$ and fix $Δ>0$. In 1989 Graham and Ringrose gave strong bounds on character sums $\sum_{M<n\leq M+N} χ(n)$ in intervals of length $N=q^Δ$ whenever $q$ is squarefree and is sufficiently smooth. Here we show that the smoothness parameter can be taken to be $N^{1-ε}$. We also discuss various generalizations and applications, obtaining best possible results in several aspects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10927 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Mixed incomplete character sums of rational functions with smooth moduli Cochrane, Todd Granville, Andrew Zheng, Junren Number Theory 11L07, 11L40 Let $χ=χ_q$ be a primitive character mod $q$ and fix $Δ>0$. In 1989 Graham and Ringrose gave strong bounds on character sums $\sum_{M<n\leq M+N} χ(n)$ in intervals of length $N=q^Δ$ whenever $q$ is squarefree and is sufficiently smooth. Here we show that the smoothness parameter can be taken to be $N^{1-ε}$. We also discuss various generalizations and applications, obtaining best possible results in several aspects. |
| title | Mixed incomplete character sums of rational functions with smooth moduli |
| topic | Number Theory 11L07, 11L40 |
| url | https://arxiv.org/abs/2601.10927 |