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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.eduandrew@math.uga.eduttucker@math.uga.edu
Andrew Granville
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602, USA, email: pcutter@kzoo.eduandrew@math.uga.eduttucker@math.uga.edu
Thomas J. Tucker
Affiliation:
Department of Mathematics, University of Georgia, Athens, Georgia 30602, USA, email: pcutter@kzoo.eduandrew@math.uga.eduttucker@math.uga.edu
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Abstract

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

References

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