Geodesic
A Family of Real Pn -Tic Fields
Canadian journal of mathematics, Tome 47 (1995) no. 3, pp. 655-672

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

Let q = p if p is an odd prime, q = 4 if p = 2. Let ζq be any primitive q-th root of unity, and let . We study the family of polynomials where Rn(X) and Sn(X) are the polynomials in the expansion We show that for fixed n, P n(X; a) is irreducible for all but finitely many a ∈ O, and for p = 3, we show that it is irreducible for all a ∈ O. The roots are all real and are permuted cyclically by a linear fractional transformation defined over the real pn-th cyclotomic field. From the roots we obtain a non-maximal set of independent units for the splitting field. In the last section we briefly treat extensions of our methods to composite p.
DOI : 10.4153/CJM-1995-034-4
Mots-clés : 11R21, 11R09, 11R16, 11R18, 11R27, pn-tic fields, units 
Shen, Yuan-Yuan; Washington, Lawrence C. A Family of Real Pn -Tic Fields. Canadian journal of mathematics, Tome 47 (1995) no. 3, pp. 655-672. doi: 10.4153/CJM-1995-034-4
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[1] 1. Cremona, J.E., Algorithms for Modular Elliptic Curves, Cambridge University Press, New York, 1992. Google Scholar

[2] 2. Gras, Marie-Nicole, Special units in real cyclic sextic fields, Math. Comp. 48(1987), 179–182. Google Scholar

[3] 3. Gras, Marie-Nicole, Familles d'unités dans les extensions cycliques réelles de degré 6 de Q, Publ. Math. Besançon, 1984.1985-1985/86. Google Scholar

[4] 4. Hemer, O., Notes on the Diophantine equation y2 — k =, x3, Ark. Mat. 3(1954), 67–77. Google Scholar

[5] 5. Lang, Serge, Algebra, Addison-Wesley, Reading, Massachusetts, 1965. Google Scholar

[6] 6. Shanks, D., The simplest cubic fields, Math. Comp. 28(1974), 1137–1152. Google Scholar

[7] 7. Shen, Y.-Y. and Washington, L.C., A family of real 2n-tic fields, to appear. Google Scholar

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