Exponential Diophantine approximation and symbolic dynamics
Number Theory
2025-01-30 v5 Dynamical Systems
Abstract
We extend the key formula which intertwines multiplicative Markoff-Lagrange spectrum and symbolic dynamics. The proof uses complex analysis and elucidates the strategy of the problem. Moreover, the new method applies to a wide variety of polynomials possibly having multiple roots. We derive several consequences of this formula, which are expected on the Markoff-Lagrange spectrum.
Cite
@article{arxiv.2204.10510,
title = {Exponential Diophantine approximation and symbolic dynamics},
author = {Shigeki Akiyama and Teturo Kamae and Hajime Kaneko},
journal= {arXiv preprint arXiv:2204.10510},
year = {2025}
}
Comments
Minor changes and corrections after the referee report