Measuring the height of a polynomial |
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Authors: | Graham Everest |
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Institution: | (1) School of Mathematics, University of East Anglia, NR4 7TJ Norwich, Norfolk, United Kingdom |
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Abstract: | Conclusions Mahler’s measure is alive and well in several quite diverse contexts. The differing points of view seem to generate a healthy
friction. If the general level of health is measured by the quantity and quality of unsolved problems, then it may help to
list these.
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Lehmer’s Problem. |
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The elliptic analogue of Lehmer, at least in tractable special cases. |
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An explanation of Boyd’s remarkable formulae. It seems thatK-theory should provide the conceptual framework. More generally, perhaps values of the elliptic Mahler measure will arise
as values of L-functions of higher-dimensional varieties.
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It looks almost certain that the elliptic Mahler measure should arise as an entropy. This would form a fascinating bridge
between two large areas of interest. Ward and I have begun to write about this 10]. At the very least, this would show that
the global canonical height of an algebraic point on an elliptic curve arises as an entropy. But of what, and what does this
mean?
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5. |
There are many other pretty results about the classical Mahler measure which could be lifted to the elliptic setting. |
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Keywords: | |
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