Results 31 to 40 of about 46,451 (125)
Modular curves, C* algebras, and chaotic cosmology [PDF]
, 2003 We make some brief remarks on the relation of the mixmaster universe model of chaotic cosmology to the geometry of modular curves and to noncommutative geometry.
Marcolli, Matilde
core +1 more source
A singular function and its relation with the number systems involved in its definition [PDF]
Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non ...
Jaume Paradís +2 more
core
Dependence with complete connections and the Gauss-Kuzmin theorem for N-continued fractions
, 2015 We consider a family $\{T_N:N \geq 1 \}$ of interval maps as generalizations of the Gauss transformation. For the continued fraction expansion arising from $T_N$, we solve its Gauss-Kuzmin-type problem by applying the theory of random systems with ...
Lascu, Dan
core +1 more source
On the concept of optimality interval [PDF]
The approximants to regular continued fractions constitute `best approximations' to the numbers they converge to in two ways known as of the first and the second kind.
Jaume Paradís +2 more
core
On the metric theory of the nearest integer continued fraction expansion
Monatshefte f�r Mathematik, 1998 Suppose \(k_n\) denotes either \(\phi(n)\) or \(\phi(p_n)\) (\(n=1,2,\dots\)), where the polynomial \(\phi\) maps the natural numbers to themselves, and \(p_k\) denote the \(k^{th}\) rational prime. Also let \(({r_n\over q_n})_{n=1}^\infty\) denote the sequence of convergents to a real number \(x\) and let \((c_n(x))_{n=1}^\infty\) be the corresponding
openaire +2 more sources
Diophantine approximation and coloring
, 2014 We demonstrate how connections between graph theory and Diophantine approximation can be used in conjunction to give simple and accessible proofs of seemingly difficult results in both subjects.Comment: 16 pages, pre-publication version of paper which ...
Haynes, Alan, Munday, Sara
core +1 more source
Scientific Bulletin of Naval Academy, 2016 A survey of the metric theory of the continued fraction expansions related to random Fibonacci Type sequences discussed by Sebe and Lascu is given. The limit properties of these expansions have been studied. A Wirsing-type approach to the Perron-Frobenius operator of the generalized Gauss map under its invariant measure allows us to get close to the ...
openaire +1 more source
On a continued fraction algorithm in finite extensions of $\Q_p$ and its metrical theory
20 ...
Choudhuri, Manoj, Makadiya, Prashant J.
openaire +2 more sources
The metrical theory of complex continued fractions [PDF]
Acta Arithmetica, 1990 openaire +1 more source
A reversible random sequence arising in the metric theory of the continued fraction expansion
Journal of Numerical Analysis and Approximation Theory, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +3 more sources