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Estimating Mahler's measure
Published online by Cambridge University Press: 17 April 2009
Abstract
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In 1962, Mahler defined a measure for integer polynomials in several variables as the logarithmic integral over the torus. Many results exist about the values taken by the measure but many unsolved problems remain. In one variable, it is possible to express the measure as an effective limit of Riemann sums. We show that the same is true in several variables, using a non-obvious parametrisation of the torus together with Baker's Theorem on linear forms in logarithms of algebraic numbers.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 51 , Issue 1 , February 1995 , pp. 145 - 151
- Copyright
- Copyright © Australian Mathematical Society 1995
References
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