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  • 1 Department of Probability Theory and Number Theory, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, LT-03225 Vilnius, Lithuania
  • | 2 Department of Mathematics, Simon Fraser University, 8888 University Drive, Burnaby BC V5A 1S6, Canada
  • | 3 Department of Mathematics, The University of British Columbia, 1984 Mathematics Road, Vancouver BC V6T 1Z2, Canada
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Abstract

A. Dubickas and C. Smyth introduced the metric Mahler measure
ea
where M(α) denotes the usual (logarithmic) Mahler measure of . This definition extends in a natural way to the t-metric Mahler measure by replacing the sum with the usual Lt norm of the vector (M(α1),…,M(αN)) for any t≧1. For α∊ℚ, we prove that the infimum in Mt(α) may be attained using only rational points, establishing an earlier conjecture of the second author. We show that the natural analogue of this result fails for general by giving an infinite family of quadratic counterexamples. As part of this construction, we provide an explicit formula to compute Mt(D1/k) for a squarefree D∊ℕ.
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Acta Mathematica Hungarica
Language English
Size B5
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Foundation
1950
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per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia
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ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

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