ISSN:
1436-5081
Keywords:
11H06
;
11H99
;
11H55
;
Distribution of lattices
;
generalized upper half plane
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Lattices Λ, Λ′ are similar if one can be transformed into the other by an angle-preserving linear map. Similarity classes of lattices of rankn may be parametrized by a fundamental domainℱ of the action ofGL n (ℤ) on the generalized upper half-plane ℋ n . Given 1〈n≤m and , letN(D,T) be the number of sublattices of ℋ n which have rankn, similarity class inD, and determinant ≤T. Our most basic result will be thatN(D,T)∼c 1(m, n)μ(D)T m asT→∞ for suitable setsD, where μ is the invariant measure on ℋ n . The casen=2 had been dealt with by Roelcke and by Maass using the theory of modular forms.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01489457
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