On values of binary quadratic forms at integer points

We obtain estimates for the number of integral solutions in large balls, of inequalities of the form \(|Q(x, y)| < \epsilon\), 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 i...

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Bibliographic Details
Published in:arXiv.org 2016-07
Main Authors: Choudhuri, Manoj, Dani, S G
Format: Article
Language:English
Subjects:
Geodesy
Quadratic forms
Online Access:Get full text
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Summary:We obtain estimates for the number of integral solutions in large balls, of inequalities of the form \(|Q(x, y)| < \epsilon\), 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 Poincare half-plane.
ISSN:2331-8422
DOI:10.48550/arxiv.1404.5163