Better than squareroot cancellation in number theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908737825931264 |
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| author | Harper, Adam J. |
| author_facet | Harper, Adam J. |
| contents | We give a short survey of the phenomenon of better than squareroot cancellation, specifically as it applies to averages of multiplicative character sums (such as $\frac{1}{r-1} \sum_{χ\; \text{mod} \; r} |\sum_{n \leq x} χ(n)|^{2q}$) thanks to their connection with so-called multiplicative chaos.
We focus on the number theoretic aspects of the arguments, and also touch on some possible applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23681 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Better than squareroot cancellation in number theory Harper, Adam J. Number Theory We give a short survey of the phenomenon of better than squareroot cancellation, specifically as it applies to averages of multiplicative character sums (such as $\frac{1}{r-1} \sum_{χ\; \text{mod} \; r} |\sum_{n \leq x} χ(n)|^{2q}$) thanks to their connection with so-called multiplicative chaos. We focus on the number theoretic aspects of the arguments, and also touch on some possible applications. |
| title | Better than squareroot cancellation in number theory |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.23681 |