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Extending Nathanson Heights to Arbitrary Finite Fields

Mario Huicochea
Published Online: 2012-08-01 | DOI: https://doi.org/10.1515/integers-2011-0127

Abstract.

In this paper, we extend the definition of the Nathanson height from points in projective spaces over to points in projective spaces over arbitrary finite fields. If , then the Nathanson height is

where with the field norm and the element of congruent to modulo p. We investigate the basic properties of this extended height, provide some bounds, study its image on the projective line and propose some questions for further research.

Keywords: Nathanson Height; Finite Field; Algebraic Closure

About the article

Received: 2010-08-11

Revised: 2012-01-12

Accepted: 2012-01-19

Published Online: 2012-08-01

Published in Print: 2012-08-01


Citation Information: Integers, Volume 12, Issue 4, Pages 669–675, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/integers-2011-0127.

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© 2012 by Walter de Gruyter Berlin Boston.Get Permission

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