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On a result of Petersson concerning the modular group

Published online by Cambridge University Press:  14 November 2011

W. W. Stothers
W. W. Stothers
Affiliation:
Department of Mathematics, University of Glasgow
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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

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References

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