Distribution of sums involving Dirichlet characters over the $k$-free integers
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910249349283840 |
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| author | Bueno, Caio |
| author_facet | Bueno, Caio |
| contents | Assuming the generalized Riemann hypothesis and a bound for the negative discrete moments of the Riemann zeta function (resp. Dirichlet $L$-functions), we prove the existence of a logarithmic limiting distribution for the normalized partial sums $x^{-\frac{1}{2k}}\sum_{n\leq x}f(n)$, where $f$ is either a quadratic Dirichlet character or a modified Dirichlet character, restricted to the $k$-free integers. Moreover, we strengthen a conjecture made by Aymone, Medeiros and the author (cf. Ramanujan J. 59(3):713-728, 2022) concerning the precise order of magnitude for these partial sums. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23100 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Distribution of sums involving Dirichlet characters over the $k$-free integers Bueno, Caio Number Theory 11L40, 11N37, 11M06 Assuming the generalized Riemann hypothesis and a bound for the negative discrete moments of the Riemann zeta function (resp. Dirichlet $L$-functions), we prove the existence of a logarithmic limiting distribution for the normalized partial sums $x^{-\frac{1}{2k}}\sum_{n\leq x}f(n)$, where $f$ is either a quadratic Dirichlet character or a modified Dirichlet character, restricted to the $k$-free integers. Moreover, we strengthen a conjecture made by Aymone, Medeiros and the author (cf. Ramanujan J. 59(3):713-728, 2022) concerning the precise order of magnitude for these partial sums. |
| title | Distribution of sums involving Dirichlet characters over the $k$-free integers |
| topic | Number Theory 11L40, 11N37, 11M06 |
| url | https://arxiv.org/abs/2602.23100 |