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Title: Growth of values of binary quadratic forms and Conway rivers
Authors: Spalding, Kathryn
Veselov, A.P.
Issue Date: 2018
Publisher: Wiley © London Mathematical Society
Citation: 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.
Abstract: We 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.
Description: 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.
Sponsor: The work of K.S. was supported by the EPSRC as part of PhD study at Loughborough
Version: Accepted for publication
DOI: 10.1112/blms.12156
URI: https://dspace.lboro.ac.uk/2134/32483
Publisher Link: https://doi.org/10.1112/blms.12156
ISSN: 1469-2120
Appears in Collections:Published Articles (Maths)

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