相关论文: On the Metrical Theory of a Generalized Continued …

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…

The metrical theory of the product of consecutive partial quotients is associated with the uniform Diophantine approximation, specifically to the improvements to Dirichlet's theorem. Achieving some variant forms of metrical theory in…

We describe various properties of continued fraction expansions of complex numbers in terms of Gaussian integers. Numerous distinct such expansions are possible for a complex number. They can be arrived at through various algorithms, as…

We prove a continued fraction expansion for the reciprocal of a certain $q$-series. All the specialists in the world are asked whether it is new or not.

The presence of large partial quotients can invalidate many classical limit theorems in the metric theory of continued fractions. A commonly employed strategy to overcome this problem is to discard the largest partial quotient when…

Many generalizations of continued fractions, where the reciprocal function has been replaced by a more general function, have been studied, and it is often asked whether such generalized expansions can have nice properties. For instance, we…

A generalization of the regular continued fractions was given by Burger et al. in 2008 [3]. In this paper we give metric properties of this expansion. For the transformation which generates this expansion, its invariant measure and…

We introduce here a general framework for studying continued fraction expansions for complex numbers and establish some results on the convergence of the corresponding sequence of convergents. For continued fraction expansions with partial…

Let x be a quadratic irrational and let P be the set of prime numbers. We show the existence of an infinite subset S of P such that the statistics of the period of the continued fraction expansions along the sequence {px: p\in S} approach…

In this paper, we introduce the polynomial continued fraction, a close relative of the well-known simple continued fraction expansions which are widely used in number theory and in general. While they may not possess all the intriguing…

We study the density of the invariant measure of the Hurwitz complex continued fraction from a computational perspective. It is known that this density is piece-wise real-analytic and so we provide a method for calculating the Taylor…

In this paper we define a new type of continued fraction expansion for a real number $x \in I_m:=[0,m-1], m\in N_+, m\geq 2$: \[x = \frac{m^{-b_1(x)}}{\displaystyle 1+\frac{m^{-b_2(x)}}{1+\ddots}}:=[b_1(x), b_2(x), ...]_m. \] Then, we…

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued…

This paper concerns extension of the classical Lagrange theorem, on the eventual periodicity of continued fraction expansions of quadratic surds, and the versions of it found in the literature in the case of complex numbers. In this…

We develop a continued fraction algorithm in finite extensions of $\Q_p$ generalising certain algorithms in $\Q_p$, and prove the finiteness property for certain small degree extensions. We also discuss the metrical properties of the…

Zaremba's conjecture concerns a formation of continued fraction expansions for rational numbers with partial quotient bounded by an absolute constant. We present asymptotic estimates for the size of $\epsilon$-thickening of certain fractal…

We give continued fraction expansions of the generating functions of Bernoulli numbers, Cauchy numbers, Euler numbers, harmonic numbers, and their generalized or related numbers. In particular, we focus on explicit forms of the convergents…

We detail the continued fraction expansion of the square root of the general monic quartic polynomial, noting that each line of the expansion corresponds to addition of the divisor at infinity. We analyse the data yielded by the general…

In an earlier paper we introduced the notion of 'bifurcating continued fractions' in a heuristic manner. In this paper a formal theory is developed for the 'bifurcating 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…