On Quadratic Fields Generated by Discriminants of Irreducible Trinomials
| dc.creator | Shparlinski, I. E. | |
| dc.date | 2008-11-08 | |
| dc.date.accessioned | 2026-07-07T10:17:06Z | |
| dc.date.available | 2026-07-07T10:17:06Z | |
| dc.description | A. Mukhopadhyay, M. R. Murty and K. Srinivas (http://arxiv.org/abs/0808.0418) have recently studied various arithmetic properties of the discriminant $Δ_n(a,b)$ of the trinomial $f_{n,a,b}(t) = t^n + at + b$, where $n \ge 5$ is a fixed integer. In particular, it is shown that, under the $abc$-conjecture, for every $n \equiv 1 \pmod 4$, the quadratic fields $\Q(\sqrt{Δ_n(a,b)})$ are pairwise distinct for a positive proportion of such discriminants with integers $a$ and $b$ such that $f_{n,a,b}$ is irreducible over $\Q$ and $|Δ_n(a,b)|\le X$, as $X\to \infty$. We use the square-sieve and bounds of character sums to obtain a weaker but unconditional version of this result. | |
| dc.identifier | https://arxiv.org/abs/0811.1300 | |
| dc.identifier | http://arxiv.org/abs/0811.1300 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173737 | |
| dc.subject | Number Theory | |
| dc.subject | 11L40; 11N36; 11R09; 11R11 | |
| dc.title | On Quadratic Fields Generated by Discriminants of Irreducible Trinomials | |
| dc.type | text |