Related papers: Open problems in geometry of continued fractions
We present a list of open questions in the theory of holomorphic foliations, possibly with singularities. Some problems have been around for a while, others are very accessible.
We present a collection of easily stated open problems in the theory of compact constant mean curvature surfaces with boundary. We also survey the current status of answering them.
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…
We consider a special class of periodic continued fractions (called alpha-fractions) and discuss the related algebraic and geometric problems. A classical description of the Jacobi variety of a hyperelliptic curve due to Jacobi naturally…
The problem of developing an arithmetic for continued fractions (in order to perform, e.g., sums and products) does not have a straightforward solution and has been addressed by several authors. In 1972, Gosper provided an algorithm to…
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…
In this paper, we investigate the monotone property of the continued fractions $G(m,\lambda)$ as a function of $m$ and $\lambda$. In particular, we obtain new inequality for the relative continued fractions.
We present a general introduction to continued fractions, with special consideration to the function fields case. These notes were prepared for a summer class given this year in Beijing at Beihang university.
In this survey paper, we present open problems and conjectures on visibility graphs of points, segments and polygons along with necessary backgrounds for understanding them.
We propose and study a generalized continued fraction algorithm that can be executed in an arbitrary imaginary quadratic field, the novelty being a non-restriction to the five Euclidean cases. Many hallmark properties of classical continued…
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…
Most well-known multidimensional continued fractions, including the M\"{o}nkemeyer map and the triangle map, are generated by repeatedly subdividing triangles. This paper constructs a family of multidimensional continued fractions by…
I give a short review of the theory of twisted symmetries of differential equations, emphasizing geometrical aspects. Some open problems are also mentioned.
This paper aims to introduce high school students to the intriguing world of continued fractions, a mathematical concept that provides a unique representation of numbers. The study focuses on the exploration and development of the…
In this work we study a problem about analytic continuation along parallel algebraic curves.
In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.
We review the open problems in the theory of deformations of zero-dimensional objects, such as algebras, modules or tensors. We list both the well-known ones and some new ones that emerge from applications. In view of many advances in…
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…
This is a collection of open problems in geometry that I think of as puzzles: they stick to my brain -- I see many grips, but no spare hands. Puzzle-charm is the only criterion for including a problem here; importance is ignored.
In this paper, an open problem in the multidimensional complex analysis is pesented that arises in the investigation of the regularity properties of Fourier integral operators and in the regularity theory for hyperbolic partial differential…