Higher Moments for Polynomial Chowla
Fuente:
arXiv
Salvato in:
| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866913473075609600 |
|---|---|
| author | Wilson, Cameron |
| author_facet | Wilson, Cameron |
| contents | Let $λ(n)$ be the Liouville function. We study the distribution of
\[
\frac{1}{x^{1/2}}\sum_{x\leq n\leq 2x}λ(f(n))
\]
over random polynomials $f$ of fixed degree $d$ and coefficients bounded in magnitude by $H$. In particular we prove that the first $d+1$ moments are Gaussian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_08726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher Moments for Polynomial Chowla Wilson, Cameron Number Theory 11A25, 11L20 Let $λ(n)$ be the Liouville function. We study the distribution of \[ \frac{1}{x^{1/2}}\sum_{x\leq n\leq 2x}λ(f(n)) \] over random polynomials $f$ of fixed degree $d$ and coefficients bounded in magnitude by $H$. In particular we prove that the first $d+1$ moments are Gaussian. |
| title | Higher Moments for Polynomial Chowla |
| topic | Number Theory 11A25, 11L20 |
| url | https://arxiv.org/abs/2408.08726 |