2 citations · 3 across the 10 of their papers we have counts for
11 papers
Quantitative Oppenheim Conjecture for Random Quadratic Forms and Optimal Variance Bounds in Function Fields
Jiyoung Han, Noy Soffer Aranov
We prove a quantitative version of Oppenheim's conjecture in the function field setting. In order to do so, we compute the higher moments of the Siegel transform. In particular, we…
Simultaneous Khintchine theorem on manifolds in positive characteristics: convergence case
Noy Soffer Aranov, Sourav Das, Arijit Ganguly +1
We prove the convergence case of Khintchine's theorem, with general approximation functions that are not necessarily monotonic, for analytic nonplanar manifolds over local fields o…
Fractals Emerging from the Toepltiz Determinants of the p-Cantor Sequence
Steven Robertson, Noy Soffer Aranov
This is the first of a pair of papers, whose collective goal is to disprove a conjecture of Kemarsky, Paulin, and Shapira (KPS) on the escape of mass of Laurent series. This paper…
Escape of Mass of the -Cantor Sequence
Noy Soffer Aranov, Steven Robertson
Let be a prime. In 2017, Kemarsky, Paulin, and Shapira (KPS) conjectured that any Laurent series over exhibits full escape of mass with respect to any irreducibl…
Minimal Denominators Lying in Subsets of the Ring of Polynomials over a Finite Field
Noy Soffer Aranov
Given a subset and fixed integers , we study the distribution of the smallest denominator for which the…
Geometric Properties of Periodic Lattices in Function Fields
Noy Soffer Aranov
Periodic lattices are natural generalizations of lattices, which arise naturally in diophantine approximations with rationals of bounded denominators. In this paper, we prove analo…
On the Minimal Denominator Problem in Function Fields
Noy Soffer Aranov
We study the minimal denominator problem in function fields. In particular, we compute the probability distribution function of the the random variable which returns the degree of…
Counting Problems for Orthogonal Sets and Sublattices in Function Fields
Noy Soffer Aranov, Angelot Behajaina
Let . Analogous to orthogonality in the Euclidean space , there exists a well-studied notion of ultrametric orthogonality in $\mat…
On the maximum size of ultrametric orthogonal sets over discrete valued fields
Noy Soffer Aranov, Angelot Behajaina
Let be a discrete valued field with finite residue field. In analogy with orthogonality in the Euclidean space , there is a well-studied notion of "ultr…
Hausdorff dimension of singular vectors in function fields
Noy Soffer Aranov, Taehyeong Kim
We compute the Hausdorff dimension of the set of singular vectors in function fields and bound the Hausdorff dimension of the set of -Dirichlet improvable vectors in t…
Counterexamples to Minkowski's Uniqueness Conjecture and Escape of Mass in Positive Characteristic
Noy Soffer Aranov
We show that there are infinitely many counterexamples to Minkowski's conjecture in positive characteristic regarding uniqueness of the upper bound of the multiplicative covering r…