Article contents
On a result of Petersson concerning the modular group
Published online by Cambridge University Press: 14 November 2011
Synopsis
Let N(u, g, h) denote the number of subgroups of index u, genus g and parabolic class number h in the classical modular group. In 1974, Petersson proved that, for g = 0 and h = 1, 2, N(u, g, h) grows exponentially with u. We obtain a formula valid for all g and h. From this we derive an asymptotic estimate, showing that Petersson's result gives the correct type of growth. The proofs use coset diagrams.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 263 - 270
- Copyright
- Copyright © Royal Society of Edinburgh 1981
References
- 4
- Cited by