Expand all Collapse all | Results 1 - 3 of 3 |
1. CJM 2011 (vol 63 pp. 1220)
Similar Sublattices of Planar Lattices The similar sublattices of a planar lattice can be classified via
its multiplier ring. The latter is the ring of rational integers in
the generic case, and an order in an imaginary quadratic field
otherwise. Several classes of examples are discussed, with special
emphasis on concrete results. In particular, we derive Dirichlet
series generating functions for the number of distinct similar
sublattices of a given index, and relate them to
zeta functions of orders in imaginary quadratic fields.
Categories:11H06, 11R11, 52C05, 82D25 |
2. CJM 2008 (vol 60 pp. 975)
An AF Algebra Associated with the Farey Tessellation We associate with the Farey tessellation of the upper
half-plane an
AF algebra $\AA$ encoding the ``cutting sequences'' that define
vertical geodesics.
The Effros--Shen AF algebras arise as quotients
of $\AA$. Using the path algebra model for AF algebras we construct, for
each $\tau \in \big(0,\frac{1}{4}\big]$, projections $(E_n)$ in
$\AA$ such that $E_n E_{n\pm 1}E_n \leq \tau E_n$.
Categories:46L05, 11A55, 11B57, 46L55, 37E05, 82B20 |
3. CJM 2004 (vol 56 pp. 77)
High-Dimensional Graphical Networks of Self-Avoiding Walks We use the lace expansion to analyse networks of mutually-avoiding
self-avoiding walks, having the topology of a graph. The networks are
defined in terms of spread-out self-avoiding walks that are permitted
to take large steps. We study the asymptotic behaviour of networks in
the limit of widely separated network branch points, and prove
Gaussian behaviour for sufficiently spread-out networks on
$\mathbb{Z}^d$ in dimensions $d>4$.
Categories:82B41, 60K35 |