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We obtain estimates for the number of integral solutions in large balls, ofinequalities of the form $|Q(x, y)| < \epsilon$, where $Q$ is an indefinitebinary quadratic form, in terms of the Hurwitz continued fraction expansions ofthe slopes of the lines on which $Q$ vanishes. The method is based on a codingof geodesics on the modular surface via Hurwitz expansions of the endpoints oftheir lifts in the Poincare half-plane.

On values of binary quadratic forms at integer points