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  • 1995-1999  (2)
  • 1965-1969
  • 11H06  (1)
  • Mathematics Subject Classification (1991):11H06  (1)
  • 1
    Electronic Resource
    Electronic Resource
    The distribution of sublattices of ℤ m (1998)
    Springer
    Monatshefte für Mathematik 125 (1998), S. 37-81 
    Details
    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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  • 2
    Electronic Resource
    Electronic Resource
    Appendix to "Approximation of viscosity solutions of elliptic partial differential equations on minimal grids", by M. Kocan: Approximation to orthogonal bases in ${\Bbb R}^n$ by orthogonal bases with integer coordinates (1995)
    Springer
    Numerische Mathematik 72 (1995), S. 117-122 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):11H06
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. In the Appendix it is shown that given $N〉1$ , an orthogonal basis $\underline{\underline {\varphi_1}},\dots, \underline{\underline{\varphi_n}}$ of ${\Bbb R}^n$ where $n\ge4$ can be approximated by an orthogonal basis $\underline{\underline{a_1}},\dots, \underline{\underline{a_n}}$ with integer components such that the angle between $\underline{\underline{\varphi_i}}$ and $\underline{\underline{a_i}}$ is at most $1/N$ $(i=1,\dots,n)$ , and $\underline{\underline {a_1}},\dots, \underline{\underline{a_n}}$ have norms $\ll N^{2n-4}$ .
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050162
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    Paper (German National Licenses)
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