Farey neighbors and hyperbolic Lorenz knots
نویسندگان
چکیده
منابع مشابه
On the distribution of Farey fractions and hyperbolic lattice points
We derive an asymptotic formula for the number of pairs of consecutive fractions a′/q′ and a/q in the Farey sequence of order Q such that a/q, q/Q, and (Q − q′)/q) lie each in prescribed subintervals of the interval [0, 1]. We deduce the leading term in the asymptotic formula for ’the hyperbolic lattice point problem’ for the modular group PSL(2,Z), the number of images of a given point under t...
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Abstract. In [7] R. F. Williams showed that all knots in the Lorenz template are prime. His proof included the cases where any number of positive twists were added to one of the template’s branches. However [7] does give an example of a composite knot in a template with a single negative twist. Below we will show that in all the negative cases composite knots do exist, and give a mechanism for ...
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ژورنال
عنوان ژورنال: Journal of Knot Theory and Its Ramifications
سال: 2017
ISSN: 0218-2165,1793-6527
DOI: 10.1142/s0218216517430040