Quintic Fields

István Gaál
Additional contact information
István Gaál: University of Debrecen, Institute of Mathematics and Informatics

Chapter 7 in Diophantine Equations and Power Integral Bases, 2002, pp 79-95 from Springer

Abstract: Abstract We had to invest the best known reduction and enumeration algorithms, many new ideas and our fastest PC-s to be able to solve index form equations in quintic fields. In the interesting case, for totally real quintic fields (with Galois group A5 or S5) this computation takes several hours, contrary to the cubic and quartic cases, where to solve the index form equation was a matter of seconds or at most some minutes. The general method is described in Section 7.1. Having read the relatively complicated formulas of this procedure, in Section 7.2 the reader is rewarded with an interesting family of totally real cyclic quintic fields introduced by E.Lehmer.

Date: 2002
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0085-7_7

Ordering information: This item can be ordered from
http://www.springer.com/9781461200857

DOI: 10.1007/978-1-4612-0085-7_7

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().