Moscow Journal of Combinatorics and Number Theory

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

Alexander Galochkin and Anastasia Godunova

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Abstract

The paper is devoted to studying how well solutions of an equation P(z,lnz)=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.

Article information

Source
Mosc. J. Comb. Number Theory, Volume 9, Number 4 (2020), 435-440.

Dates
Received: 30 December 2019
Revised: 11 February 2020
Accepted: 25 February 2020
First available in Project Euclid: 12 November 2020

Permanent link to this document
https://projecteuclid.org/euclid.moscow/1605150028

Digital Object Identifier
doi:10.2140/moscow.2020.9.435

Mathematical Reviews number (MathSciNet)
MR4170707

Zentralblatt MATH identifier
07272360

Subjects
Primary: 11J82: Measures of irrationality and of transcendence

Keywords
Diophantine approximation algebraic numbers logarithms

Citation

Galochkin, Alexander; Godunova, Anastasia. On approximations of solutions of the equation $P(z,\ln z)=0$ by algebraic numbers. Mosc. J. Comb. Number Theory 9 (2020), no. 4, 435--440. doi:10.2140/moscow.2020.9.435. https://projecteuclid.org/euclid.moscow/1605150028


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References

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