A note on the least totient of a residue class
| dc.creator | Garaev, M. Z. | |
| dc.date | 2007-11-14 | |
| dc.date | 2007-11-19 | |
| dc.date.accessioned | 2026-07-07T08:43:19Z | |
| dc.date.available | 2026-07-07T08:43:19Z | |
| dc.description | Let $q$ be a large prime number, $a$ be any integer, $ε$ be a fixed small positive quantity. Friedlander and Shparlinksi \cite{FSh} have shown that there exists a positive integer $n\ll q^{5/2+ε}$ such that $ϕ(n)$ falls into the residue class $a \pmod q.$ Here, $ϕ(n)$ denotes Euler's function. In the present paper we improve this bound to $n\ll q^{2+ε}.$ | |
| dc.description | Improved version | |
| dc.identifier | https://arxiv.org/abs/0711.2240 | |
| dc.identifier | http://arxiv.org/abs/0711.2240 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/142271 | |
| dc.subject | Number Theory | |
| dc.subject | 11L40 | |
| dc.title | A note on the least totient of a residue class | |
| dc.type | text |