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ON THE ELLIPTIC ANALOGUE OF JENSEN'S FORMULA

Published online by Cambridge University Press:  01 February 1999

G. R. EVEREST
G. R. EVEREST
Affiliation:
School of Mathematics, University of East Anglia, Norwich, Norfolk NR4 7TJ. E-mail: [email protected]
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Abstract

Mahler's measure of a polynomial can be written as a logarithmic integral over the torus. We propose a definition when the underlying group is an elliptic curve. Having reviewed some of the classical results in the toral case, we take some first steps towards realising elliptic analogues. In particular, we focus on elliptic analogues of Kronecker's theorem and Lehmer's problem. We wish to stress the fundamental role played by Jensen's formula in both the toral and elliptic formulations of these results.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 21 - 36
Copyright
The London Mathematical Society 1999

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