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


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.


Algebraic Number Mahler Measure Nonzero Algebraic Number 
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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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