6 citations · 12 across the 11 of their papers we have counts for
19 papers · 1 filter
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…
Rational Points and Brownian Motion
Faustin Adiceam, Volodymyr Pavlenkov, Evgeniy Zorin
Given a real-valued function , let be the number of rational points with denominators at most in the -tubular neighbourhood of the graph of…
On the -adic Littlewood Conjecture in Characteristics
Faustin Adiceam, Dzmitry Badziahin
Given a prime , the -adic Littlewood Conjecture stands as a well-known arithmetic variant of the celebrated Littlewood Conjecture in Diophantine Approximation. In the same wa…
Probabilistic Effectivity in the Subspace Theorem
Faustin Adiceam, Victor Shirandami
The Subspace Theorem due to Schmidt (1972) is a broad generalisation of Roth's Theorem in Diophantine Approximation (1955) which, in the same way as the latter, suffers a notorious…
Homogeneous Forms Inequalities
Faustin Adiceam, Oscar Marmon
Given a set of inequalities determined by homogeneous forms, the following intertwined results are established: (1) the volume of the real semi-algebraic domain determined by these…
Rational points close to non-singular algebraic curves
Faustin Adiceam, Oscar Marmon
We study the density of solutions to Diophantine inequalities involving non-singular ternary forms, or equivalently, the density of rational points close to non-singular plane alge…
Visibility Properties of Spiral Sets
Faustin Adiceam, Ioannis Tsokanos
A spiral in is defined as a set of the form where is a sph…
Around the Danzer Problem and the Construction of Dense Forests
Faustin Adiceam
A 1965 problem due to Danzer asks whether there exists a set with finite density in Euclidean space intersecting any convex body of volume one. A suitable weakening of the volume c…
Higher Dimensional Spiral Delone Sets
Faustin Adiceam, Ioannis Tsokanos
A Delone set in is a set such that (a) the distance between any two of its points is uniformly bounded below by a strictly positive constant and such that (b) the di…
Cut-and-project quasicrystals, lattices, and dense forests
Faustin Adiceam, Yaar Solomon, Barak Weiss
Dense forests are discrete subsets of Euclidean space which are uniformly close to all sufficiently long line segments. The degree of density of a dense forest is measured by its v…
On the -adic Littlewood Conjecture
Faustin Adiceam, Erez Nesharim, Fred Lunnon
The -adic Littlewood Conjecture due to De Mathan and Teulié asserts that for any prime number and any real number , the equation $$\inf_{|m|\ge 1} |m|\cdot |m|_p\cdot |\l…
On the Minimum of a Positive Definite Quadratic Form over Non--Zero Lattice points. Theory and Applications
Faustin Adiceam, Evgeniy Zorin
Let be the set of positive definite matrices with determinant 1 in dimension . Identifying any two -congruent elements in gives rise…
How far can you see in a forest?
Faustin Adiceam
We address a visibility problem posed by Solomon & Weiss. More precisely, in any dimension , we construct a forest $\F$ with finite density satisfying the followi…
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…
Rational approximation and arithmetic progressions
Faustin Adiceam
A reasonably complete theory of the approximation of an irrational by rational fractions whose numerators and denominators lie in prescribed arithmetic progressions is developed in…
Liminf Sets in Simultaneous Diophantine Approximation
Faustin Adiceam
Let Q be an infinite set of positive integers. Denote by W(Q) the set of n-tuples of real numbers simultaneously tau-well approximable by infinitely many rationals with denominator…
Vertical shift and simultaneous Diophantine approximation on polynomial curves
Faustin Adiceam
The Hausdorff dimension of the set of simultaneously tau well approximable points lying on a curve defined by a polynomial P(X)+alpha, where P(X) is a polynomial with integer coeff…
A note on the Hausdorff dimension of some liminf sets appearing in simultaneous Diophantine approximation
Faustin Adiceam
Let Q be an infinite set of positive integers. Denote by W_{τ, n}(Q) (resp. W_{τ, n}) the set of points in dimension n simultaneously τ--approximable by infinitely many rationals w…
An Extension of a Theorem of Duffin and Schaeffer in Diophantine Approximation
Faustin Adiceam
Duffin and Schaeffer have generalized the classical theorem of Khintchine in metric Diophantine approximation in the case of any error function under the assumption that all the ra…