Vol. 7, No. 5, 2014

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The complement of Fermat curves in the plane

Seth Dutter, Melissa Haire and Ariel Setniker

Vol. 7 (2014), No. 5, 611–618
Abstract

In this paper we will examine the affine algebraic curves defined on the complement of Fermat curves of degree five or higher in the affine plane. In particular we will bound the height of integral points over an affine curve outside of an exceptional set.

Keywords
Mason's theorem, function field, Fermat curve
Mathematical Subject Classification 2010
Primary: 14G25
Milestones
Received: 31 August 2012
Revised: 20 January 2013
Accepted: 21 January 2013
Published: 1 August 2014

Communicated by Bjorn Poonen
Authors
Seth Dutter
Department of Mathematics, Statistics and Computer Science
University of Wisconsin-Stout
Menomonie, WI 54751
United States
Melissa Haire
Department of Mathematics and Computer Science
Gordon College
Wenham, MA 01984
United States
Ariel Setniker
Mathematics Department
Western Oregon University
Monmouth, OR 97361
United States