A relationship between the Mahler measure and the discriminant of algebraic numbers
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.
KeywordsAlgebraic Number Mahler Measure Nonzero Algebraic Number
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