314 research outputs found
Projections in Rotation Algebras and Theta Functions
For each , denotes the universal -algebra
generated by two unitaries and , which satisfy the commutation relation
. We consider the order four automorphism of
defined by , and describe a method
for constructing projections in the fixed point algebra ,
using Rieffel's imprimitivity bimodules and Jacobi's theta functions. In the
case , , , we give explicit formulae
for such projections and find a lower bound for the norm of the Harper operator
.Comment: Fixes some numerical issues in the published versio
On certain statistical properties of continued fractions with even and with odd partial quotients
We prove results concerning the joint limiting distribution of the renewal
time of denominators and consecutive digits of random irrational numbers in the
case of continued fractions with even partial quotients, with odd partial
quotients, and for Nakada's \alpha-expansions.Comment: Final versio
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