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Abstract
The paper is devoted to studying how well solutions of an equation
P ( z , ln z )
= 0 , where
P ( x , y )
∈
ℤ [ x , y ] , can
be approximated with algebraic numbers. We prove a new bound with the help of a
construction due to K. Mahler.
Keywords
Diophantine approximation, algebraic numbers, logarithms
Mathematical Subject Classification 2010
Primary: 11J82
Milestones
Received: 30 December 2019
Revised: 11 February 2020
Accepted: 25 February 2020
Published: 5 November 2020