Discriminants of Chebyshev Radical Extensions
Number Theory
2013-06-10 v2
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.
Keywords
Cite
@article{arxiv.1304.6055,
title = {Discriminants of Chebyshev Radical Extensions},
author = {Thomas Alden Gassert},
journal= {arXiv preprint arXiv:1304.6055},
year = {2013}
}
Comments
This update contains proofs for the conjectures appearing in a earlier version of this paper. This article draws heavily from arXiv:0906.2629