Continued Fractions and Series
نویسندگان
چکیده
منابع مشابه
Beta-continued Fractions over Laurent Series
The present paper is devoted to a new notion of continued fractions in the field of Laurent series over a finite field. The definition of this kind of continued fraction algorithm is based on a general notion of number systems. We will prove some ergodic properties and compute the Hausdorff dimensions of bounded type continued fraction sets.
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We investigate when an algebraic function of the form φ(λ) = −B(λ)+ √ R(λ) A(λ) , where R(λ) is a polynomial of odd degree N = 2g + 1 with coefficients in C, can be written as a periodic α-fraction of the form
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Given a continued fraction, we construct a certain function that is discontinuous at every rational number p/q. We call this discontinuity the “gap”. We then try to characterize the gap sizes, and find, to the first order, the size is 1/q2, and that, for higher orders, the gap appears to be perfectly ’randomly’ distributed, in that it is Cauchy-dense on the unit square, and thus, this function ...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1995
ISSN: 0022-314X
DOI: 10.1006/jnth.1995.1121