Markov and Lagrange spectra for Laurent series in $1/T$ with rational coefficients

Abstract

Nikoleta Kalaydzhieva (London) 1. Introduction. A binary quadratic form q with real coefficients a, b, c given by q = q(x, y) := ax 2 + bxy + cy 2 has discriminant d(q) = b 2 − 4ac and arithmetic minimum M (q) = inf x,y∈Z (x,y) =(0,0) |q(x, y)|.Considering an appropriate normalisation of these minima yields a set of real numbers, called the Markov spectrum: