Vol. 9, No. 4, 2020

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On approximations of solutions of the equation $P(z,\ln z)=0$ by algebraic numbers

Alexander Galochkin and Anastasia Godunova

Vol. 9 (2020), No. 4, 435–440
Abstract

The paper is devoted to studying how well solutions of an equation P(z,lnz) = 0, where P(x,y) [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
Authors
Alexander Galochkin
Department of Number Theory
Moscow Lomonosov State University
Moscow
Russia
Anastasia Godunova
Department of Number Theory
Moscow Lomonosov State University
Moscow
Russia