Noy Soffer Aranov

activity

20242026

collaborators

10 papers

math.NT2026

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…

math.NT2026

Minimal Denominators Lying in Subsets of the Ring of Polynomials over a Finite Field

Noy Soffer Aranov

Given a subset $S \subseteq F_{q} [x]$ and fixed integers $n, m \in N$ , we study the distribution of the smallest denominator $Q \in S$ for which the…

math.NT2026

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…

math.CO2026

Counting Problems for Orthogonal Sets and Sublattices in Function Fields

Noy Soffer Aranov, Angelot Behajaina

Let $K = F_{q} ((x^{- 1}))$ . Analogous to orthogonality in the Euclidean space $R^{n}$ , there exists a well-studied notion of ultrametric orthogonality in $\mat…

math.NT2025

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…

math.NT2025

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…