Rational functions invariant under a finite abelian group

Lenstra, H.W.

doi:10.1007/bf01389732

Cited by 148 publications

(111 citation statements)

References 33 publications

Supporting

Mentioning

107

Contrasting

Unclassified

Order By: Relevance

“…[6]). It is known that Noether's problem for C e has a positive answer for e ≤ 7, although it has in many cases negative answers (see [16], [10], [6]). Replacing i, j by each other and equating the right-hand sides, we obtain (iv).…”

Section: Geometric Generalization Of Gaussian Period Relationsmentioning

confidence: 99%

Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations

Hashimoto

Hoshi

2005

Math. Comp.

View full text Add to dashboard Cite

Abstract. 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. Using this, we obtain explicit multi-parametric families of cyclic polynomials over Q of degree 3 ≤ e ≤ 7. We also give a simple family of cyclic polynomials with one parameter in each case, by specializing our parameters.

show abstract

Section: Geometric Generalization Of Gaussian Period Relationsmentioning

confidence: 99%

Families of cyclic polynomials obtained from geometric generalization of Gaussian period relations

Hashimoto

Hoshi

2005

Math. Comp.

View full text Add to dashboard Cite

show abstract

“…Apply [L,Proposition 1.3] to the field l = C(M ) and the l-vector space W = lr i , where {r i } is a Z-basis for R which is permuted by G. Then there exists elements {y i } in W G which form an L-basis for W . Now W ⊂ l(R), and hence…”

Section: Definitionsmentioning

confidence: 99%

Induction theorems on the stable rationality of the center of the ring of generic matrices

Beneish

1998

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. Following Procesi and Formanek, the center of the division ring of n × n generic matrices over the complex numbers C is stably equivalent to the fixed field under the action of Sn, of the function field of the group algebra of a ZSn-lattice, denoted by Gn. We study the question of the stable rationality of the center Cn over the complex numbers when n is a prime, in this module theoretic setting. Let N be the normalizer of an n-sylow subgroup of Sn. Let M be a ZSn-lattice. We show that under certain conditions on M , inductionrestriction from N to Sn does not affect the stable type of the corresponding field. In particular, C(Gn) and C(ZG ⊗ ZN Gn) are stably isomorphic and the isomorphism preserves the Sn-action. We further reduce the problem to the study of the localization of Gn at the prime n; all other primes behave well. We also present new simple proofs for the stable rationality of Cn over C, in the cases n = 5 and n = 7.

show abstract

“…Les résultats de ce paragraphe sont essentiellement dus, moyennant parfois quelques traductions (voir à ce sujet §2, R 6), à Lenstra [18], Endo-Miyata [12] et Voskresenskiï ([33], [35]), mais la présentation et les démonstrations (notamment celle figurant à la proposition 3) sont parfois différentes. La présentation adoptée ici, strictement algébrique, a l'avantage d'être complètement dégagée de considérations géométriques ou birationnelles.…”

Section: Modules Et Résolutions Flasquesunclassified

“…Soient H un sous-groupe fermé de G et Res la restriction usuelle J^G-^-^H-Soit ^ l'une quelconque des propriétés (iv) à (ix) du lemme 2, ou même la propriété (j) : Le lemme 3 ci-dessous, facile, mais important pour la suite, est déjà utilisé par Lenstra [18] (démonstration de la proposition 1.2). LEMME 3 [12].…”

Section: Remarquesunclassified