QUINTIC POLYNOMIALS OF HASHIMOTO–TSUNOGAI, BRUMER AND KUMMER

Masanari Kida (1) , Guénaël Renault (2) , Kazuhiro Yokoyama (3)

1 UEC - University of Electro-Communications [Tokyo]
2 SALSA - Solvers for Algebraic Systems and Applications
3 Department of Mathematics [Rikkyo]

We establish an isomorphism between the quintic cyclic polynomi-als discovered by Hashimoto-Tsunogai and those arising from Kummer theory for certain algebraic tori. This enables us to solve the isomorphism problem for Hashimoto-Tsunogai polynomials and also Brumer's quintic polynomials.

Domaines: Calcul formel [cs.SC]; Théorie des nombres [math.NT]

Masanari Kida, Guénaël Renault, Kazuhiro Yokoyama. QUINTIC POLYNOMIALS OF HASHIMOTO–TSUNOGAI, BRUMER AND KUMMER. International Journal of Number Theory, 2009, 05 (4), pp.555 - 571. ⟨10.1142/S1793042109002250⟩. ⟨hal-01099030⟩