On a number-theoretic result of Zsigmondy in domains of quadratic integers (Q1104975)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On a number-theoretic result of Zsigmondy in domains of quadratic integers |
scientific article; zbMATH DE number 4057626
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a number-theoretic result of Zsigmondy in domains of quadratic integers |
scientific article; zbMATH DE number 4057626 |
Statements
On a number-theoretic result of Zsigmondy in domains of quadratic integers (English)
0 references
1989
0 references
By the help of new lower estimates for values of cyclotomic polynomials, a new approach to the generalized theorem of Zsigmondy on the existence of prime ideals \(P\) in domains of quadratic integers \(\mathfrak O_K\) fulfilling \(\mathrm{ord}_P(e)=n\) (e\(\in\mathfrak O_K\), \(n\in\mathbb{N})\) is presented. This improves earlier results of \textit{L. Rédei} [Acta Sci. Math. 19, 98--126 (1958; Zbl 0085.02502)], \textit{H. Sachs} [Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg 6, 223--260 (1957; Zbl 0079.26802)] and \textit{G. Drauschke} and \textit{M. Tasche} [Arch. Math. 49, 292--300 (1987; Zbl 0611.12001)].
0 references
lower estimates for values of cyclotomic polynomials
0 references
quadratic integers
0 references
0.91127336
0 references
0.90621567
0 references
0.90285766
0 references
0.9012186
0 references
0.8945237
0 references
0.89353013
0 references
