Growth of values of binary quadratic forms and Conway rivers
journal contribution
posted on 2018-04-06, 13:24 authored by Kathryn Spalding, Alexander VeselovAlexander VeselovWe study the growth of the values of integer binary quadratic forms Q on a binary planar tree as it was described by Conway. We show that the corresponding Lyapunov exponents _Q(x) as a function of the path determined by x 2 RP1 are twice the values of the
corresponding exponents for the growth of Markov numbers [10], except for the paths corresponding to the Conway river, when _Q(x) = 0: The relation with the Galois result about pure periodic continued fractions is explained and interpreted geometrically.
Funding
The work of K.S. was supported by the EPSRC as part of PhD study at Loughborough
History
School
- Science
Department
- Mathematical Sciences
Published in
Bulletin of the London Mathematical SocietyCitation
SPALDING, K. and VESELOV, A.P., 2018. Growth of values of binary quadratic forms and Conway rivers. Bulletin of the London Mathematical Society, 50 (3), pp.513-528.Publisher
Wiley © London Mathematical SocietyVersion
- AM (Accepted Manuscript)
Publisher statement
This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/Acceptance date
2018-03-06Publication date
2018-04-16Notes
This is the peer reviewed version of the following article: SPALDING, K. and VESELOV, A.P., 2018. Growth of values of binary quadratic forms and Conway rivers. Bulletin of the London Mathematical Society, 50 (3), pp.513-528, which has been published in final form at https://doi.org/10.1112/blms.12156. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.ISSN
1469-2120Publisher version
Language
- en
