相关论文: Palindromic continued fractions

Using Schmidt's Subspace Theorem, this paper improves and extends an existing transcendence result for sequences of algebraic numbers. The theorems thus produced correspond to a central theorem on the irrationality of sequences due to…

We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…

We present a detailed Hausdorff dimension analysis of the set of real numbers where the product of consecutive partial quotients in their continued fraction expansion grow at a certain rate but the growth of the single partial quotient is…

We consider a family of integer sequences generated by nonlinear recurrences of the second order, which have the curious property that the terms of the sequence, and integer multiples of the ratios of successive terms (which are also…

Symmetrical subdivisions in the space of Jager Pairs for continued fractions-like expansions will provide us with bounds on their difference. Results will also apply to the classical regular and backwards continued fractions expansions,…

This paper investigates integer multiplication of continued fractions using geometric structures. In particular, this paper shows that integer multiplication of a continued fraction can be represented by replacing one triangulation of an…

Let $[a_1(x),a_2(x),a_3(x),\cdots]$ be the continued fraction expansion of $x\in (0,1)$. This paper is concerned with certain sets of continued fractions with non-decreasing partial quotients. As a main result, we obtain the Hausdorff…

The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization…

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…

In this paper we show how to apply various techniques and theorems (including Pincherle's theorem, an extension of Euler's formula equating infinite series and continued fractions, an extension of the corresponding transformation that…

In this paper, we clarified the relationship between continued fractions, determinants, and identities, making it easier to apply these methods systematically in other settings. In particular, we studied finite continued fractions from the…

The main purpose of this article is to introduce some new binomial difference sequence spaces of fractional order ${\tilde{\alpha}} $ along with infinite matrices. Some topological properties of these spaces are considered along with the…

For integers $m \geq 2$, we study divergent continued fractions whose numerators and denominators in each of the $m$ arithmetic progressions modulo $m$ converge. Special cases give, among other things, an infinite sequence of divergence…

Our main result is that any real cubic algebraic number has a continued fraction expansion with polynomial coefficients. Some generalizations are mentioned.

We detail the continued fraction expansion of the square root of a monic polynomials of even degree. We note that each step of the expansion corresponds to addition of the divisor at infinity, and interpret the data yielded by the general…

Large and moderate deviation principles are proved for Engel continued fractions, a new type of continued fraction expansion with non-decreasing partial quotients in number theory.

We establish an equidistribution result for push-forwards of certain locally finite algebraic measures in the adelic extension of the space of lattices in the plane. As an application of our analysis we obtain new results regarding the…

This paper is a sequel to our previous paper arXiv:1105.1554, where we defined two types of intermediate Diophantine exponents, connected them to Schmidt exponents and split Dyson's transference inequality into a chain of inequalities for…

The continued fraction expansion of an irrational number $\alpha$ is eventually periodic if and only if $\alpha$ is a quadratic irrationality. However, very little is known regarding the size of the partial quotients of algebraic real…

In this note, we describe a family of particular algebraic, and nonquadratic, power series over an arbitrary finite field of characteristic 2, having a continued fraction expansion with all partial quotients of degree one. The main purpose…