Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-30T18:23:42.244Z Has data issue: false hasContentIssue false
  • English
  • Français

The Number of Fields Generated by the Square Root of Values of a Given Polynomial

Published online by Cambridge University Press:  20 November 2018

Pamela Cutter ,
Andrew Granville  and
Thomas J. Tucker
Pamela Cutter
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602, USA, email: pcutter@kzoo.edu andrew@math.uga.edu ttucker@math.uga.edu
Andrew Granville
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602, USA, email: pcutter@kzoo.edu andrew@math.uga.edu ttucker@math.uga.edu
Thomas J. Tucker
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602, USA, email: pcutter@kzoo.edu andrew@math.uga.edu ttucker@math.uga.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The $abc$ -conjecture is applied to various questions involving the number of distinct fields $\mathbb{Q}\left( \sqrt{f(n)} \right)$ , as we vary over integers $n$ .

Keywords

11N3211D41

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 1 , 01 March 2003 , pp. 71 - 79
Copyright
Copyright © Canadian Mathematical Society 2003

References

[1] Bombieri, E., Effective Diophantine Approximation on Gm . Ann. Scuola Norm. Pisa Cl. Sci (4) 20 (1993), 61–89.Google Scholar
[2] Elkies, N., ABC implies Mordell. Internat.Math. Res. Notices 7 (1991), 99–109.Google Scholar
[3] Granville, A., ABC means we can count squarefrees. Internat.Math. Res. Notices 19 (1998), 991–1009.Google Scholar
[4] Halberstam, H. and Richert, H.-E., Sieve Methods. Academic Press, London-New York-San Francisco, 1974.Google Scholar
[5] Hooley, C., On the power free values of polynomials. Mathematika 14 (1967), 21–26.Google Scholar
[6] Siegel, C. L., Über einege Anwendungen diophantischer Approximaten. Abh. Preuss. Akad.Wiss. Phys. Math. Kl. 1 (1929), 209–266.Google Scholar