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# Mathematical Research Letters

## Volume 22 (2015)

### Number 4

### On values of binary quadratic forms at integer points

Pages: 1023 – 1045

DOI: https://dx.doi.org/10.4310/MRL.2015.v22.n4.a4

#### Authors

#### Abstract

We obtain estimates for the number of integral solutions in large balls, of inequalities of the form $\lvert Q(x, y) \rvert \lt \epsilon$, where $Q$ is an indefinite binary quadratic form, in terms of the Hurwitz continued fraction expansions of the slopes of the lines on which $Q$ vanishes. The method is based on a coding of geodesics on the modular surface via Hurwitz expansions of the endpoints of their lifts in the Poincaré half-plane.

Accepted 19 September 2014

Published 24 July 2015