Vol. 9, No. 4, 2020

Download this article
Download this article For screen
For printing
Recent Issues
Volume 12, Issue 3
Volume 12, Issue 2
Volume 12, Issue 1
Volume 11, Issue 4
Volume 11, Issue 3
Volume 11, Issue 2
Volume 11, Issue 1
Volume 10, Issue 4
Volume 10, Issue 3
Volume 10, Issue 2
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
Older Issues
Volume 7, Issue 4
Volume 7, Issue 3
Volume 7, Issue 2
Volume 7, Issue 1
Volume 6, Issue 4
Volume 6, Issue 2-3
Volume 6, Issue 1
Volume 5, Issue 4
Volume 5, Issue 3
Volume 5, Issue 1-2
Volume 4, Issue 4
Volume 4, Issue 3
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 3-4
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 4
Volume 2, Issue 3
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 4
Volume 1, Issue 3
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
founded and published with the
scientific support and advice of
mathematicians from the
Moscow Institute of
Physics and Technology
 
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Author Index
To Appear
 
Other MSP Journals
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