Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

This is probably an easy question, but I can't seem get the right idea so here goes: Let $\tau \in \mathfrak{h}$ (where $\mathfrak{h}$ denotes the upper halfplane) be given. For any two positive real numbers $M_1 < M_2$, I am interested in calculating $$ |\{ \gamma \in SL_2(\mathbb{Z}) \ | \ M_1 < \frac{\Re(\gamma.\tau)}{\Im(\gamma.\tau)} < M_2 \ \}|$$ where $\gamma$ acts by fractional linear transformation. Any thoughts would be appreciated. Of course non-trivial upper/lower bounds would be of interest as well.

share|improve this question
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.