On partial derivatives of some summatory functions
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915851346640896 |
|---|---|
| author | Tenenbaum, Gérald |
| author_facet | Tenenbaum, Gérald |
| contents | Let $f$ be a real arithmetic function and let $g:[1,\infty[\to{\mathbb R}$ be a smooth function. We describe two emblematic instances in which saddle-point estimates may be used to evaluate the frequency, on the set of integers $n\leqslant x$, of the event $\{f(n)\leqslant g(n)\}$ from those relevant to the event $\{f(n)\leqslant y\}$. The first example revisits Dickman's historical contribution to the theory of friable integers. The second is concerned with the distribution of the squarefree kernel of an integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_04584 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On partial derivatives of some summatory functions Tenenbaum, Gérald Number Theory 11N25, 11N37, 11K65, secondary 11N35, 11N64 Let $f$ be a real arithmetic function and let $g:[1,\infty[\to{\mathbb R}$ be a smooth function. We describe two emblematic instances in which saddle-point estimates may be used to evaluate the frequency, on the set of integers $n\leqslant x$, of the event $\{f(n)\leqslant g(n)\}$ from those relevant to the event $\{f(n)\leqslant y\}$. The first example revisits Dickman's historical contribution to the theory of friable integers. The second is concerned with the distribution of the squarefree kernel of an integer. |
| title | On partial derivatives of some summatory functions |
| topic | Number Theory 11N25, 11N37, 11K65, secondary 11N35, 11N64 |
| url | https://arxiv.org/abs/2407.04584 |