On primitive Dirichlet characters and the Riemann hypothesis
| dc.creator | Banks, William D. | |
| dc.creator | Guloglu, Ahmet M. | |
| dc.creator | Nevans, C. Wesley | |
| dc.date | 2008-06-24 | |
| dc.date.accessioned | 2026-07-07T09:46:26Z | |
| dc.date.available | 2026-07-07T09:46:26Z | |
| dc.description | For any natural number $n$, let $X'_n$ be the set of primitive Dirichlet characters modulo $n$. We show that if the Riemann hypothesis is true, then the inequality $|X'_{2n_k}|\le C_2 e^{-γ} ϕ(2n_k)/\log\log(2n_k)$ holds for all $k\ge 1$, where $n_k$ is the product of the first $k$ primes, $γ$ is the Euler-Mascheroni constant, $C_2$ is the twin prime constant, and $ϕ(n)$ is the Euler function. On the other hand, if the Riemann hypothesis is false, then there are infinitely many $k$ for which the same inequality holds and infinitely many $k$ for which it fails to hold. | |
| dc.description | 7 pages | |
| dc.identifier | https://arxiv.org/abs/0806.3944 | |
| dc.identifier | http://arxiv.org/abs/0806.3944 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/163529 | |
| dc.subject | Number Theory | |
| dc.subject | 11N37 | |
| dc.title | On primitive Dirichlet characters and the Riemann hypothesis | |
| dc.type | text |