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arXiv · 1511.01295

Galois structure on integral valued polynomials

Bahar Heidaryan·Matteo Longo·Giulio Peruginelli
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Abstract

We characterize finite Galois extensions $K$ of the field of rational numbers in terms of the rings ${\rm Int}_{\mathbb{Q}}(\mathcal O_K)$, recently introduced by Loper and Werner, consisting of those polynomials which have coefficients in $\mathbb{Q}$ and such that $f(\mathcal O_K)$ is contained in $\mathcal O_K$. We also address the problem of constructing a basis for ${\rm Int}_{\mathbb{Q}}(\mathcal O_K)$ as a $\mathbb{Z}$-module.

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Bahar Heidaryan, Matteo Longo, Giulio Peruginelli. 2016-08-29. Galois structure on integral valued polynomials. https://doi.org/10.1016/j.jnt.2016.07.007

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