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Mathematical Notes

, Volume 59, Issue 3, pp 293–297 | Cite as

A relationship between the Mahler measure and the discriminant of algebraic numbers

  • E. M. Matveev
Article

Abstract

In this note we show that in the well-known Dobrowolski estimate lnM(α) ≫ (ln lnd/ lnd)3,d → ∞, whereα is a nonzero algebraic number of degreed that is not a root of unity andM(α) is its Mahler measure, the parameterd can be replaced by the quantityδ=d/Δ(α)1/d, where Δ(α) is the modulus of the discriminant ofα. To this end,α must satisfy the condition degαp=degα for any primep.

Keywords

Algebraic Number Mahler Measure Nonzero Algebraic Number 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • E. M. Matveev
    • 1
  1. 1.Moscow State Textile AcademyUSSR

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