A sightly improved classical transcendence measure for \(e\) will be given, by showing that the absolute constant in Mahler's measure can be taken to be 1 . We also give an improved linear independence measure for the system \(1, e, \ldots, e^{n}\). fr 1995 Academic Press. Inc
AnABCinequality for Mahler’s measure
✍ Scribed by Jeffrey D. Vaaler
- Book ID
- 106198654
- Publisher
- Springer Vienna
- Year
- 2008
- Tongue
- English
- Weight
- 167 KB
- Volume
- 154
- Category
- Article
- ISSN
- 0026-9255
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We define a new height function on the group of non-zero algebraic numbers :, the height of : being the infimum over all products of Mahler measures of algebraic numbers whose product is :. We call this height the metric Mahler measure, since its logarithm defines a metric in the factor group of the
The Mahler measures of some n-variable polynomial families are given in terms of special values of the Riemann zeta function and a Dirichlet L-series, generalizing the results of Lalín (J. Number Theory 103 (2003) 85-108). The technique introduced in this work also motivates certain identities among