Vol. 3, No. 4, 2010

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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