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arXiv · 1304.6055

Discriminants of Chebyshev Radical Extensions

Thomas Alden Gassert
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Abstract

Let t be any integer and fix an odd prime ell. Let Phi(x) = T_ell^n(x)-t denote the n-fold composition of the Chebyshev polynomial of degree ell shifted by t. If this polynomial is irreducible, let K = bbq(theta), where theta is a root of Phi. A theorem of Dedekind's gives a condition on t for which K is monogenic. For other values of t, we apply the Montes algorithm to obtain a formula for the discriminant of K and to compute basis elements for the ring of integers O_K.

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Thomas Alden Gassert. 2013-06-07. Discriminants of Chebyshev Radical Extensions. https://arxiv.org/abs/1304.6055

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