The $L^1$ mean of the exponential sum of the divisor function
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916773272485888 |
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| author | Parry, Tomos |
| author_facet | Parry, Tomos |
| contents | We give a relatively simple proof that \[ \int _0^1\left |\sum _{n\leq x}d(n)e(nα)\right |dα\asymp \sqrt x.\] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04747 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $L^1$ mean of the exponential sum of the divisor function Parry, Tomos Number Theory We give a relatively simple proof that \[ \int _0^1\left |\sum _{n\leq x}d(n)e(nα)\right |dα\asymp \sqrt x.\] |
| title | The $L^1$ mean of the exponential sum of the divisor function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2404.04747 |