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Journal of the London Mathematical Society 1998 58(1):1-8; doi:10.1112/S0024610798006577
© 1998 by London Mathematical Society
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© The London Mathematical Society

Bounding the Elliptic Mahler Measure II

Graham Everest and Chris Pinner

School of Mathematics, University of East Anglia Norwich, Norfolk NR4 7TJ. E-mail: g.everest{at}uea.ac.uk
Department of Mathematics and Computer Science, University of Northern British Columbia 3333 University Way, Prince George, BC V2N 4Z9, Canada. E-mail: pinnerc{at}unbc.ca

Received 29 January 1996. Revision received 20 June 1996.

The theory of heights for rational points on arithmetic elliptic curves is becoming well known. An important fact in the basic theory is the relationship between the naïve and the canonical height of a rational point; in fact, they differ by a uniformly bounded amount. The paper provides a generalisation of this fact from the point of view of heights of polynomials, rather than heights of points. This concept is extended to polynomials in several variables.


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