Large values of shifted mixed character sums
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911681514307584 |
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| author | Tardy, Néo |
| author_facet | Tardy, Néo |
| contents | We consider sums of the form $$F_χ(α,β;θ) := \sum_{αp<n\leβp}χ(n)e(nθ),$$ where $χ$ is a non-principal Dirichlet character modulo a prime number $p$. We prove that $$ \sqrt p \log \log p \ll \max_{0 \le θ< 1}{\left|F_χ(α,β;θ)\right|} \ll \sqrt{p}\log p, $$ generalizing an old result of Montgomery as well as a recent result of Iggidr in two aspects: we allow general non-principal characters $χ$, and we consider incomplete mixed character sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13715 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Large values of shifted mixed character sums Tardy, Néo Number Theory Classical Analysis and ODEs 11C08, 11L40, 42A05 We consider sums of the form $$F_χ(α,β;θ) := \sum_{αp<n\leβp}χ(n)e(nθ),$$ where $χ$ is a non-principal Dirichlet character modulo a prime number $p$. We prove that $$ \sqrt p \log \log p \ll \max_{0 \le θ< 1}{\left|F_χ(α,β;θ)\right|} \ll \sqrt{p}\log p, $$ generalizing an old result of Montgomery as well as a recent result of Iggidr in two aspects: we allow general non-principal characters $χ$, and we consider incomplete mixed character sums. |
| title | Large values of shifted mixed character sums |
| topic | Number Theory Classical Analysis and ODEs 11C08, 11L40, 42A05 |
| url | https://arxiv.org/abs/2605.13715 |