On values of binary quadratic forms at integer points

被引：3

作者：

Choudhuri, Manoj ^{[1
]}

Dani, S. G. ^{[2
]}

机构：

[1] Tata Inst Fundamental Res, Ctr Applicable Math, Bangalore 560065, Karnataka, India

[2] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India

来源：

MATHEMATICAL RESEARCH LETTERS | 2015年 / 22卷 / 04期

关键词：

D O I：

10.4310/MRL.2015.v22.n4.a4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain estimates for the number of integral solutions in large balls, of inequalities of the form vertical bar Q(x, y)vertical bar < 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.

引用

页码：1023 / 1045

页数：23