Geodesic
The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X 5 + aX + b
Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 138-153

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

Let ${{X}^{5}}\,+\,aX\,+\,b\,\in \,Z\left[ X \right]$ have Galois group ${{D}_{5}}$ . Let $\theta $ be a root of ${{X}^{5}}\,+\,aX\,+\,b$ . An explicit formula is given for the discriminant of $Q\left( \theta\right)$ .
DOI : 10.4153/CMB-2002-017-8
Mots-clés : 11R21, 11R29, dihedral quintic field, trinomial, discriminant 
Spearman, Blair K.; Williams, Kenneth S. The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X 5 + aX + b. Canadian mathematical bulletin, Tome 45 (2002) no. 1, pp. 138-153. doi: 10.4153/CMB-2002-017-8
@article{10_4153_CMB_2002_017_8,
     author = {Spearman, Blair K. and Williams, Kenneth S.},
     title = {The {Discriminant} of a {Dihedral} {Quintic} {Field} {Defined} by a {Trinomial} {X} 5 + {aX} + b},
     journal = {Canadian mathematical bulletin},
     pages = {138--153},
     year = {2002},
     volume = {45},
     number = {1},
     doi = {10.4153/CMB-2002-017-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-017-8/}
}
TY  - JOUR
AU  - Spearman, Blair K.
AU  - Williams, Kenneth S.
TI  - The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X 5 + aX + b
JO  - Canadian mathematical bulletin
PY  - 2002
SP  - 138
EP  - 153
VL  - 45
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-017-8/
DO  - 10.4153/CMB-2002-017-8
ID  - 10_4153_CMB_2002_017_8
ER  - 
%0 Journal Article
%A Spearman, Blair K.
%A Williams, Kenneth S.
%T The Discriminant of a Dihedral Quintic Field Defined by a Trinomial X 5 + aX + b
%J Canadian mathematical bulletin
%D 2002
%P 138-153
%V 45
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2002-017-8/
%R 10.4153/CMB-2002-017-8
%F 10_4153_CMB_2002_017_8

[1] [1] Liu, D., Dihedral polynomial congruences and binary quadratic forms: a class field theory approach. Ph.D. thesis, Carleton University, Ottawa, Ontario, Canada, 1992. Google Scholar

[2] [2] Llorente, P., Nart, E. and Vila, N., Discriminants of number fields defined by trinomials. Acta Arith. 43 (1984), 367–373. Google Scholar

[3] [3] Marcus, D. A., Number Fields. Springer-Verlag, New York-Heidelberg-Berlin, 1977. Google Scholar

[4] [4] Roland, G., Yui, N. and Zagier, D., A parametric family of quintic polynomials with Galois group D5. J. Number Theory 15 (1982), 137–142. Google Scholar

Cité par Sources :