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Journal of the London Mathematical Society 1999 59(1):21-36; doi:10.1112/S0024610799007097
© 1999 by London Mathematical Society
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© The London Mathematical Society

On the Elliptic Analogue of Jensen's Formula

G. R. Everest

School of Mathematics, University of East Anglia Norwich, Norfolk NR4 7TJ. E-mail: g.everest{at}uea.ac.uk

Received 12 September 1996.

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.


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