Vol. 3, No. 4, 2010

Download this article
Download this article For screen
For printing
Recent Issues

Volume 11, 1 issue

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editors’ Addresses
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Some conjectures on the maximal height of divisors of $x^n-1$

Nathan C. Ryan, Bryan C. Ward and Ryan Ward

Vol. 3 (2010), No. 4, 451–457
Abstract

Define B(n) to be the largest height of a polynomial in [x] dividing xn 1. We formulate a number of conjectures related to the value of B(n) when n is of a prescribed form. Additionally, we prove a lower bound for B(n).

Keywords
cyclotomic polynomials, heights
Mathematical Subject Classification 2000
Primary: 11C08, 11Y70, 12Y05
Milestones
Received: 29 September 2010
Revised: 23 November 2010
Accepted: 1 December 2010
Published: 6 January 2011

Communicated by Kenneth S. Berenhaut
Authors
Nathan C. Ryan
Department of Mathematics
Bucknell University
Lewisburg, PA 17837
United States
Bryan C. Ward
Department of Mathematics
Bucknell University
Lewisburg, PA 17837
United States
Ryan Ward
Department of Mathematics
Bucknell University
Lewisburg, PA 17837
United States