Geodesic
The Number of Fields Generated by the Square Root of Values of a Given Polynomial
Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 71-79

Voir la notice de l'article provenant de la source Cambridge University Press

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 $n$ .
DOI : 10.4153/CMB-2003-007-0
Mots-clés : 11N32, 11D41 
Cutter, Pamela; Granville, Andrew; Tucker, Thomas J. The Number of Fields Generated by the Square Root of Values of a Given Polynomial. Canadian mathematical bulletin, Tome 46 (2003) no. 1, pp. 71-79. doi: 10.4153/CMB-2003-007-0
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[1] [1] Bombieri, E., Effective Diophantine Approximation on G . Ann. Scuola Norm. Pisa Cl. Sci (4) 20 (1993), 61–89. Google Scholar

[2] [2] Elkies, N., ABC implies Mordell. Internat.Math. Res. Notices 7 (1991), 99–109. Google Scholar

[3] [3] Granville, A., ABC means we can count squarefrees. Internat.Math. Res. Notices 19 (1998), 991–1009. Google Scholar

[4] [4] Halberstam, H. and Richert, H.-E., Sieve Methods. Academic Press, London-New York-San Francisco, 1974. Google Scholar

[5] [5] Hooley, C., On the power free values of polynomials. Mathematika 14 (1967), 21–26. Google Scholar

[6] [6] Siegel, C. L., Über einege Anwendungen diophantischer Approximaten. Abh. Preuss. Akad.Wiss. Phys. Math. Kl. 1 (1929), 209–266. Google Scholar

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