Generalised Markov numbers
Number Theory
2018-09-07 v1
Abstract
In this paper we introduce generalised Markov numbers and extend the classical Markov theory for the discrete Markov spectrum to the case of generalised Markov numbers. In particular we show recursive properties for these numbers and find corresponding values in the Markov spectrum. Further we construct a counterexample to the generalised Markov uniqueness conjecture. The proposed generalisation is based on geometry of numbers. It substantively uses lattice trigonometry and geometric theory of continued numbers.
Cite
@article{arxiv.1809.01688,
title = {Generalised Markov numbers},
author = {Oleg Karpenkov and Matty van-Son},
journal= {arXiv preprint arXiv:1809.01688},
year = {2018}
}
Comments
50 pages