Translator Disclaimer
March 2021 Monogenic Cyclotomic compositions
Joshua Harrington, Lenny Jones
Author Affiliations +
Kodai Math. J. 44(1): 115-125 (March 2021). DOI: 10.2996/kmj44107

Abstract

Let $m$ and $n$ be positive integers, and let $p$ be a prime. Let $T(x)=\Phi_{p^m}(\Phi_{2^n}(x))$, where $\Phi_k(x)$ is the cyclotomic polynomial of index $k$. In this article, we prove that $T(x)$ is irreducible over $\mathbf Q$ and that

$\left\{1,\theta,\theta^2,\ldots,\theta^{2^{n-1}p^{m-1}(p-1)-1}\right\}$

is a basis for the ring of integers of $\mathbf Q (\theta)$, where $T(\theta)= 0$.

Citation

Download Citation

Joshua Harrington. Lenny Jones. "Monogenic Cyclotomic compositions." Kodai Math. J. 44 (1) 115 - 125, March 2021. https://doi.org/10.2996/kmj44107

Information

Received: 25 July 2019; Revised: 5 September 2020; Published: March 2021
First available in Project Euclid: 23 March 2021

Digital Object Identifier: 10.2996/kmj44107

Subjects:
Primary: 11R04
Secondary: 11R09 , 11R32 , 12F12

Keywords: composition , cyclotomic polynomial , irreducible , Monogenic

Rights: Copyright © 2021 Tokyo Institute of Technology, Department of Mathematics

JOURNAL ARTICLE
11 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.44 • No. 1 • March 2021
Back to Top