Almost sure upper bound for random multiplicative functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910568359657472 |
|---|---|
| author | Caich, Rachid |
| author_facet | Caich, Rachid |
| contents | Let $\varepsilon >0$. Let $f$ be a Steinhaus or Rademacher random multiplicative function. We prove that we have almost surely, as $x \to +\infty$,
$$
\sum_{n \leqslant x} f(n) \ll \sqrt{x} (\log_2 x)^{\frac{3}{4}+ \varepsilon}.
$$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_00943 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Almost sure upper bound for random multiplicative functions Caich, Rachid Number Theory Probability Let $\varepsilon >0$. Let $f$ be a Steinhaus or Rademacher random multiplicative function. We prove that we have almost surely, as $x \to +\infty$, $$ \sum_{n \leqslant x} f(n) \ll \sqrt{x} (\log_2 x)^{\frac{3}{4}+ \varepsilon}. $$ |
| title | Almost sure upper bound for random multiplicative functions |
| topic | Number Theory Probability |
| url | https://arxiv.org/abs/2304.00943 |