Harper's beyond square-root conjecture
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909784610963456 |
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| author | Wang, Victor Y. Xu, Max Wenqiang |
| author_facet | Wang, Victor Y. Xu, Max Wenqiang |
| contents | We explain how the (shifted) Ratios Conjecture for $L(s,χ)$ would extend a randomization argument of Harper from a conductor-limited range to an unlimited range of ``beyond square-root cancellation'' for character twists of the Liouville function. As a corollary, the Liouville function would have nontrivial cancellation in arithmetic progressions of modulus just exceeding the well-known square-root barrier. Morally, the paper passes from random matrices to random multiplicative functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_04094 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Harper's beyond square-root conjecture Wang, Victor Y. Xu, Max Wenqiang Number Theory Probability We explain how the (shifted) Ratios Conjecture for $L(s,χ)$ would extend a randomization argument of Harper from a conductor-limited range to an unlimited range of ``beyond square-root cancellation'' for character twists of the Liouville function. As a corollary, the Liouville function would have nontrivial cancellation in arithmetic progressions of modulus just exceeding the well-known square-root barrier. Morally, the paper passes from random matrices to random multiplicative functions. |
| title | Harper's beyond square-root conjecture |
| topic | Number Theory Probability |
| url | https://arxiv.org/abs/2405.04094 |