A note on a result of Mahler's

Abstract

In a recent paper, Maher [2] proved that for any algebraic number field K of degree n and discriminant d there exists a constant C depending only on n and d such that for any ceiling λP of K there exists a basis α₁ ..., α_n of the corresponding ideal α_λ such that C^-(n-1)λ(q) ≤ |α_k|_q ≤ Cλ(q) for all q; C^-n λ(τ) ≤ |α_k|_τ ≤ λ(τ) for all r; (k = 1, 2, ..., n).