969,576 research outputs found
Integers and Fractions
This article briefly reviews the quantum Hall effect and the contributions of
the winners of the 1998 Nobel Prize in Physics.Comment: LaTeX, 6 pages, no figures. On the 1998 Nobel Prize in Physics. To
appear in Current Scienc
Palindromic continued fractions
In the present work, we investigate real numbers whose sequence of partial
quotients enjoys some combinatorial properties involving the notion of
palindrome. We provide three new transendence criteria, that apply to a broad
class of continued fraction expansions, including expansions with unbounded
partial quotients. Their proofs heavily depend on the Schmidt Subspace Theorem
Commensurable continued fractions
We compare two families of continued fractions algorithms, the symmetrized
Rosen algorithm and the Veech algorithm. Each of these algorithms expands real
numbers in terms of certain algebraic integers. We give explicit models of the
natural extension of the maps associated with these algorithms; prove that
these natural extensions are in fact conjugate to the first return map of the
geodesic flow on a related surface; and, deduce that, up to a conjugacy, almost
every real number has an infinite number of common approximants for both
algorithms.Comment: 41 pages, 10 figure
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