The distribution of smooth numbers in arithmetic progressions
| dc.creator | Soundararajan, K. | |
| dc.date | 2007-07-02 | |
| dc.date.accessioned | 2026-07-07T08:13:42Z | |
| dc.date.available | 2026-07-07T08:13:42Z | |
| dc.description | For a wide range of $x$ and $y$ we show that ${\Cal S}(x,y)$, the set of integers below $x$ composed only of prime factors below $y$, is equidistributed in the reduced residue classes $\pmod q$ for all $q<y^{4\sqrt{e}-ε}$. This improves earlier work of Granville; any improvement of this range of $q$ would have interesting consequences for Vinogradov's conjecture on the least quadratic non-residue. For larger ranges of $q$ we prove the existence of a large subgroup of the group of reduced residues such that ${\Cal S}(x,y)$ is equidistributed within cosets of that subgroup. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/0707.0299 | |
| dc.identifier | http://arxiv.org/abs/0707.0299 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/132859 | |
| dc.subject | Number Theory | |
| dc.title | The distribution of smooth numbers in arithmetic progressions | |
| dc.type | text |