A k-automorphism Ïƒ of the rational function field k(x1, . . . , xn) is called purely monomial if Ïƒ sends every variable xi to a monic Laurent monomial in the variables x1, . . . , xn. Let G be aâ€¦ (More)

A general method of constructing families of cyclic polynomials over Q with more than one parameter will be discussed, which may be called a geometric generalization of the Gaussian period relations.â€¦ (More)

We study Noetherâ€™s problem for various subgroups H of the normalizer of a group C8 generated by an 8-cycle in S8, the symmetric group of degree 8, in three aspects according to the way they act onâ€¦ (More)

We study the field isomorphism problem of cubic generic polynomial X + sX + s over the field of rational numbers with the specialization of the parameter s to nonzero rational integers m viaâ€¦ (More)

We study Noetherâ€™s problem for various subgroups H of the normalizer of a group C8 generated by an 8-cycle in S8, the symmetric group of degree 8, in three aspects according to the way they act onâ€¦ (More)

Let K be any field, K(x1, . . . , xn) be the rational function field of n variables over K, and Sn and An be the symmetric group and the alternating group of degree n respectively. For any a âˆˆ K \â€¦ (More)

Let k be any field, k(x, y) be the rational function field of two variables over k. Let Ïƒ be a k-automorphism of k(x, y) defined by Ïƒ(x) = âˆ’x(3x âˆ’ 9y âˆ’ y) (27x + 2x + 9xy + 2xy âˆ’ y) , Ïƒ(y) = âˆ’(3x +â€¦ (More)

We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X âˆ’ mXY âˆ’ (m + 3)XY 2 âˆ’ Y 3 = k where k | m + 3m + 9 and non-isomorphic simplest cubic fields. Byâ€¦ (More)

We give a correspondence between non-trivial solutions to a parametric family of cubic Thue equations X âˆ’ mXY âˆ’ (m + 3)XY 2 âˆ’ Y 3 = k where k | m +3m+9 and isomorphic simplest cubic fields. Byâ€¦ (More)