On the Sum of Reciprocals of Primes
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_ | 1866908367717400576 |
|---|---|
| author | Kim, Young Deuk |
| author_facet | Kim, Young Deuk |
| contents | Suppose that $y>0$, $0\leqα<2π$, and $0<K<1$. Let $P^+$ be the set of primes $p$ such that $\cos(y\ln p+α)>K$ and $P^-$ the set of primes $p$ such that $\cos(y\ln p+α)<-K$. In this paper, we prove $\sum_{p\in P^+}\frac{1}{p}=\infty$ and $\sum_{p\in P^-}\frac{1}{p}=\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04768 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Sum of Reciprocals of Primes Kim, Young Deuk General Mathematics 11N05 Suppose that $y>0$, $0\leqα<2π$, and $0<K<1$. Let $P^+$ be the set of primes $p$ such that $\cos(y\ln p+α)>K$ and $P^-$ the set of primes $p$ such that $\cos(y\ln p+α)<-K$. In this paper, we prove $\sum_{p\in P^+}\frac{1}{p}=\infty$ and $\sum_{p\in P^-}\frac{1}{p}=\infty$. |
| title | On the Sum of Reciprocals of Primes |
| topic | General Mathematics 11N05 |
| url | https://arxiv.org/abs/2403.04768 |