Remarks on the Selberg--Delange method
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2020
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908417427243008 |
|---|---|
| author | de la Bretèche, Régis Tenenbaum, Gérald |
| author_facet | de la Bretèche, Régis Tenenbaum, Gérald |
| contents | Let $\varrho$ be a complex number and let $f$ be a multiplicative arithmetic function whose Dirichlet series takes the form $ζ(s)^\varrho G(s)$, where $G$ is associated to a multiplicative function $g$. The classical Selberg-Delange method furnishes asymptotic estimates for averages of $f$ under assumptions of either analytic continuation for $G$, or absolute convergence of a finite number of derivatives of $G(s)$ at $s=1$. We consider different set of hypotheses, not directly comparable to the previous ones, and investigate how they can yield sharp asymptotic estimates for the averages of~$f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_12929 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Remarks on the Selberg--Delange method de la Bretèche, Régis Tenenbaum, Gérald Number Theory 11N37 Let $\varrho$ be a complex number and let $f$ be a multiplicative arithmetic function whose Dirichlet series takes the form $ζ(s)^\varrho G(s)$, where $G$ is associated to a multiplicative function $g$. The classical Selberg-Delange method furnishes asymptotic estimates for averages of $f$ under assumptions of either analytic continuation for $G$, or absolute convergence of a finite number of derivatives of $G(s)$ at $s=1$. We consider different set of hypotheses, not directly comparable to the previous ones, and investigate how they can yield sharp asymptotic estimates for the averages of~$f$. |
| title | Remarks on the Selberg--Delange method |
| topic | Number Theory 11N37 |
| url | https://arxiv.org/abs/2010.12929 |