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- W4302182487 abstract "E. Thomas was one of the first to solve an infinite family of Thue equations, when he considered the forms $F_n(X, Y )= X^3 -(n-1)X^2Y -(n+2)XY^2 -Y^3$ and the family of equations $F_n(X, Y )=pm 1$, $nin {mathbf N}$. This family is associated to the family of the simplest cubic fields ${mathbf Q}(lambda)$ of D. Shanks, $lambda$ being a root of $F_n(X,1)$. We introduce in this family a second parameter by replacing the roots of the minimal polynomial $F_n(X, 1) $ of $lambda$ by the $a$-th powers of the roots and we effectively solve the family of Thue equations that we obtain and which depends now on the two parameters $n$ and $a$." @default.
- W4302182487 created "2022-10-06" @default.
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- W4302182487 date "2015-05-25" @default.
- W4302182487 modified "2023-10-17" @default.
- W4302182487 title "A family of Thue equations involving powers of units of the simplest cubic fields" @default.
- W4302182487 doi "https://doi.org/10.48550/arxiv.1505.06708" @default.
- W4302182487 hasPublicationYear "2015" @default.
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