E. Zorin

activity

20102026

most citedDiophantine approximation on curves and the distribution of rational points: divergence theory

5 citations · 18 across the 14 of their papers we have counts for

collaborators

23 papers

math.NT2026

Rational Points near Monofractal Curves and the Strong Oscillation Principle

Faustin Adiceam, Volodymyr Pavlenkov, Evgeniy Zorin

In their previous work devoted to the distribution of rational points near Brownian motion, the authors conjectured the existence of an \emph{oscillation principle} governing the a…

math.NT2026

Kronecker sequences beyond the torus: nearest-neighbour distances and best returns

Evgeniy Zorin

We study nearest-neighbour distances and strict best returns of cyclic orbits on $(V \times G) /Λ$ , where $V$ is a finite-dimensional real normed space, $G$ has a bi-invariant ultram…

math.NT2026

Positive Logarithmic Hausdorff Measures of Exceptional Sets for the $p$ -adic and $t$ -adic Littlewood Conjectures

Dzmitry Badziahin, Volodymyr Pavlenkov, Evgeniy Zorin

We prove that if the exceptional set $E_{p}$ for the $p$ -adic Littlewood conjecture is non-empty, then its logarithmic Hausdorff dimension is at least one. More precisely, whenever $…

math.NT2026

Rational Points and Brownian Motion

Faustin Adiceam, Volodymyr Pavlenkov, Evgeniy Zorin

Given a real-valued function $f$ , let $N_{f} (δ, Q)$ be the number of rational points with denominators at most $Q \geq 1$ in the $(δ / Q)$ -tubular neighbourhood of the graph of…

math.NT2024★ 1 cited

Diophantine approximation and the Mass Transference Principle: incorporating the unbounded setup

Bing Li, Lingmin Liao, Baowei Wnag +2

We develop the Mass Transference Principle for rectangles of Wang \& Wu (Math. Ann. 2021) to incorporate the `unbounded' setup; that is, when along some direction the lower order (…

math.NT2024

Inhomogeneous Diophantine Approximation on $M_{0}$ -sets

Volodymyr Pavlenkov, Evgeniy Zorin

We prove new quantitative Schmidt-type theorem for Diophantine approximations with restraint denominators on fractals (more precisely, on $M_{0}$ -sets). Our theorems introduce a shar…

math.NT2023

Inhomogeneous Kaufman Measures and Diophantine Approximation

Sam Chow, Agamemnon Zafeiropoulos, Evgeniy Zorin

We introduce an inhomogeneous variant of Kaufman's measure, with applications to diophantine approximation. In particular, we make progress towards a problem related to Littlewood'…

math.NT2022★ 1 cited

The Shrinking Target Problem for Matrix Transformations of Tori: revisiting the standard problem

Bing Li, Lingmin Liao, Sanju Velani +2

Let $T$ be a $d \times d$ matrix with real coefficients. Then $T$ determines a self-map of the $d$ -dimensional torus $T^{d} = R^{d} / Z^{d}$ . Let $ \{E_n \}_{n \in \m…

math.NT2019★ 4 cited

Inhomogeneous Diophantine Approximation on $M_{0}$ -sets with restricted denominators

Andrew D. Pollington, Sanju Velani, Agamemnon Zafeiropoulos +1

Let $F \subseteq [0, 1]$ be a set that supports a probability measure $μ$ with the property that $∣ μ (t) ∣ ≪ (lo g ∣ t ∣)^{- A}$ for some constant $A > 0$ . Let $\mathcal{A}=…

math.NT2018★ 5 cited

Diophantine approximation on curves and the distribution of rational points: divergence theory

V. Beresnevich, R. C. Vaughan, S. Velani +1

In this paper we develop a new explicit method to studying rational points near manifolds and obtain optimal lower bounds on the number of rational points of bounded height lying a…

math.NT2017

On irrationality measure of Thue-Morse constant

Dzmitry Badziahin, Evgeniy Zorin

We provide a non-trivial measure of irrationality for a class of Mahler numbers defined with infinite products which cover the Thue-Morse constant.

math.NT2016

On the Minimum of a Positive Definite Quadratic Form over Non--Zero Lattice points. Theory and Applications

Faustin Adiceam, Evgeniy Zorin

Let $Σ_{d}^{++}$ be the set of positive definite matrices with determinant 1 in dimension $d \geq 2$ . Identifying any two $S L_{d} (Z)$ -congruent elements in $Σ_{d}^{++}$ gives rise…

math.NT2015

On generalized Thue-Morse functions and their values

Dzmitry Badziahin, Evgeny Zorin

This paper naturally extends and generalizes our previous work "Thue-Morse constant is not badly approximable", arXiv:1407.3182 [math.NT]. Here we consider the Laurent series $f_d(…

math.NT2015

Diophantine Approximation and applications in Interference Alignment

Faustin Adiceam, Victor Beresnevich, Jason Levesley +2

This paper is motivated by recent applications of Diophantine approximation in electronics, in particular, in the rapidly developing area of Interference Alignment. Some remarkable…

math.NT2015

Diophantine approximation on manifolds and the distribution of rational points: contributions to the convergence theory

Victor Beresnevich, Robert C. Vaughan, Sanju Velani +1

In this paper we develop the convergence theory of simultaneous, inhomogeneous Diophantine approximation on manifolds. A consequence of our main result is that if the manifold $M \…

math.NT2014

On the Mixed Littlewood Conjecture and continued fractions in quadratic fields

Paloma Bengoechea, Evgeniy Zorin

We show how a recent result by Aka and Shapira on the evolution of continued fractions in a fixed quadratic field implies the classic result of de Mathan and Teullié on the Mixed L…

math.NT2014

Thue-Morse constant is not badly approximable

Dzmitry Badziahin, Evgeniy Zorin

We prove that Thue-Morse constant $τ_{T M} = 0.01101001.. ._{2}$ is not a badly approximable number. Moreover, we prove that $τ_{T M} (a) = 0.01101001.. ._{a}$ is not badly approximable for eve…

math.NT2013★ 1 cited

Algebraic independence and normality of the values of Mahler's functions

Evgeniy Zorin

The main purpose of this article is to provide new results on algebraic independence of values of Mahler functions and their generalizations. Simultaneously, we establish new measu…

math.NT2012★ 1 cited

Multiplicity Estimates for Algebraically Dependent Analytic Functions

Evgeniy Zorin

We prove a new general multiplicity estimate applicable to sets of functions without any assumption on algebraic independence. The multiplicity estimates are commonly used in deter…

math.NT2011

Multiplicity estimate for solutions of extended Ramanujan's system

Evgeniy Zorin

We establish a new multiplicity lemma for solutions of a differential system extending Ramanujan's classical differential relations. This result can be useful in the study of arith…

math.NT2011★ 2 cited

Algebraic Independence and Mahler's method

Evgeniy Zorin

We give some new results on algebraic independence within Mahler's method, including algebraic independence of values at transcendental points. We also give some new measures of al…

math.NT2011★ 3 cited

Zero Order Estimates for Analytic Functions

Evgeniy Zorin

The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under so…

math.NT2010

Explicit bounds for rational points near planar curves and metric Diophantine approximation

Victor Beresnevich, Evgeniy Zorin

The primary goal of this paper is to complete the theory of metric Diophantine approximation initially developed in [Ann. of Math.(2) 166 (2007), p.367-426] for $C^{3}$ non-degenerat…

Rational Points near Monofractal Curves and the Strong Oscillation Principle

Kronecker sequences beyond the torus: nearest-neighbour distances and best returns

Positive Logarithmic Hausdorff Measures of Exceptional Sets for the p-adic and t-adic Littlewood Conjectures

Rational Points and Brownian Motion

Diophantine approximation and the Mass Transference Principle: incorporating the unbounded setup

Inhomogeneous Diophantine Approximation on M0​-sets

Inhomogeneous Kaufman Measures and Diophantine Approximation

The Shrinking Target Problem for Matrix Transformations of Tori: revisiting the standard problem

Inhomogeneous Diophantine Approximation on M0​-sets with restricted denominators

Diophantine approximation on curves and the distribution of rational points: divergence theory

On irrationality measure of Thue-Morse constant

On the Minimum of a Positive Definite Quadratic Form over Non--Zero Lattice points. Theory and Applications

On generalized Thue-Morse functions and their values

Diophantine Approximation and applications in Interference Alignment

Diophantine approximation on manifolds and the distribution of rational points: contributions to the convergence theory

On the Mixed Littlewood Conjecture and continued fractions in quadratic fields

Thue-Morse constant is not badly approximable

Algebraic independence and normality of the values of Mahler's functions

Multiplicity Estimates for Algebraically Dependent Analytic Functions

Multiplicity estimate for solutions of extended Ramanujan's system

Algebraic Independence and Mahler's method

Zero Order Estimates for Analytic Functions

Explicit bounds for rational points near planar curves and metric Diophantine approximation

Positive Logarithmic Hausdorff Measures of Exceptional Sets for the $p$ -adic and $t$ -adic Littlewood Conjectures

Inhomogeneous Diophantine Approximation on $M_{0}$ -sets

Inhomogeneous Diophantine Approximation on $M_{0}$ -sets with restricted denominators