Strange and pseudo-differentiable functions with applications to prime partitions
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866908343531995136 |
|---|---|
| author | Dong, Anji Robles, Nicolas Zaharescu, Alexandru Zeindler, Dirk |
| author_facet | Dong, Anji Robles, Nicolas Zaharescu, Alexandru Zeindler, Dirk |
| contents | Let $\mathfrak{p}_{\mathbb{P}_r}(n)$ denote the number of partitions of $n$ into $r$-full primes. We use the Hardy-Littlewood circle method to find the asymptotic of $\mathfrak{p}_{\mathbb{P}_r}(n)$ as $n \to \infty$. This extends previous results in the literature of partitions into primes. We also show an analogue result involving convolutions of von Mangoldt functions and the zeros of the Riemann zeta-function. To handle the resulting non-principal major arcs we introduce the definition of strange functions and pseudo-differentiability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20102 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strange and pseudo-differentiable functions with applications to prime partitions Dong, Anji Robles, Nicolas Zaharescu, Alexandru Zeindler, Dirk Number Theory Primary: 11P55, 11P82, 26A24. Secondary: 11L07, 11L20, 11M26 Let $\mathfrak{p}_{\mathbb{P}_r}(n)$ denote the number of partitions of $n$ into $r$-full primes. We use the Hardy-Littlewood circle method to find the asymptotic of $\mathfrak{p}_{\mathbb{P}_r}(n)$ as $n \to \infty$. This extends previous results in the literature of partitions into primes. We also show an analogue result involving convolutions of von Mangoldt functions and the zeros of the Riemann zeta-function. To handle the resulting non-principal major arcs we introduce the definition of strange functions and pseudo-differentiability. |
| title | Strange and pseudo-differentiable functions with applications to prime partitions |
| topic | Number Theory Primary: 11P55, 11P82, 26A24. Secondary: 11L07, 11L20, 11M26 |
| url | https://arxiv.org/abs/2412.20102 |