Related papers: Nearest lambda_q-multiple fractions

We study the Hp-Lq boundedness of certain integral operators of fractional type.

The connection between cutting sequences of geodesics on the modular surface $\operatorname{PSL}(2,\mathbb{Z})\backslash\mathbb{H}$ and regular continued fractions was established by Series, and Heersink expanded the cross-section of the…

In this paper we study the common distance between points and the behavior of a constant length step discrete random walk on finite area hyperbolic surfaces. We show that if the second smallest eigenvalue of the Laplacian is at least 1/4,…

A recent continuous family of multiplicity functions on local rings was introduced by Taylor interpolating between Hilbert-Samuel and Hilbert-Kunz multiplicities. The obvious goal is to use this as a tool for deforming results from one to…

The nearest integer continued fraction of a real number $x$ from $[-1/2, 1/2)$ is defined. Some metrical properties of these expansions are presented. We define the approximation coefficients and give an important result on them. The main…

We extend the Series' connection between the modular surface $\mathcal{M}=\operatorname{PSL}(2,\mathbb{Z})\backslash\mathbb{H}$, cutting sequences, and regular continued fractions to the slow converging Lehner and Farey continued fractions…

Let $P(a,q)$ be the least prime in the arithmetic progression $\{n\equiv a(mod\ q)\}$. In this note, when $q$ has bounded cubic part and $(a,q)=1$, we combine the Heath-Brown's method and the Burgess's bounds for L-functions to obtain $…

We prove a two-parameter family of continued fraction identities for $\arctan(p/q)$, where $p$ and $q$ are positive integers with $p\le q$. For every such pair, the identity \[ \arctan\frac{p}{q} =…

We construct Lipschitz $Q$-valued functions which approximate carefully integral currents when their cylindrical excess is small and they are almost minimizing in a suitable sense. This result is used in two subsequent works to prove the…

We explore basic properties and some applications of Quasi Differential Quotients ($QDQ$s) and the related $QDQ$-approximating multi-cones. A $QDQ$, which is a special kind of H.Sussmann's Approximate Generalized Differential Quotient…

In this work we study qualitative properties of real analytic bounded maps. The main tool is approximation of real valued functions analytic in rectangular domains of the complex plane by continued g-fractions of Wall. As an application,…

We study the problem of best approximations of a vector $\alpha\in{\mathbb R}^n$ by rational vectors of a lattice $\Lambda\subset {\mathbb R}^n$ whose common denominator is bounded. To this end we introduce successive minima for a periodic…

The Gauss-Kuzmin statistics for the triangle map (a type of multidimensional continued fraction algorithm) are derived by examining the leading eigenfunction of the triangle map's transfer operator. The technical difficulty is finding the…

Let G=SO(n,1) and Gamma a geometrically finite Zariski dense subgroup of G which is contained in an arithmetic subgroup of G. Denoting by Gamma(q) the principal congruence subgroup of Gamma of level q, and fixing a positive number \lambda_0…

For a partially multiplicative quandle (PMQ) $\mathcal{Q}$ we consider the topological monoid $\mathring{\mathrm{HM}}(\mathcal{Q})$ of Hurwitz spaces of configurations in the plane with local monodromies in $\mathcal{Q}$. We compute the…

In this paper we establish a congruence on the degree of the map from a component of a Hurwitz space of covers of elliptic curves to the moduli stack of elliptic curves. Combinatorially, this can be expressed as a congruence on the…

This paper is a short survey of the recent results on examples of periodic two-dimensional continued fractions (in Klein's model). In the last part of this paper we formulate some questions, problems and conjectures on geometrical…

We introduce a general framework to study the local dynamics of near-parabolic maps using the meromorphic $1$-form introduced by X.~Buff. As a sample application of this setup, we prove the following tameness result on invariant curves of…

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let G' be an appropriate neat arithmetic subgroup of G. We present two algorithms to compute the action of the Hecke operators on the…

In this article, we have introduced (p;q)-variant of Stancu-Schurer operators and discussed the rate of convergence for continuous functions. We have also discussed recursive estimates Korovkin and direct approximation results using second…