Noy Soffer Aranov - Academia.edu (original) (raw)

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Papers by Noy Soffer Aranov

Deleted Journal, May 16, 2024

We show that there are infinitely many counterexamples to Minkowski's conjecture in posit... more 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 radius, µ, by constructing a sequence of compact A orbits where µ obtains its conjectured upper bound. In addition, we show that these orbits, as well as a slightly larger sequence of orbits, must exhibit complete escape of mass.

arXiv (Cornell University), May 18, 2024

We compute the Hausdorff dimension of the set of singular vectors in function fields and bound th... more We compute the Hausdorff dimension of the set of singular vectors in function fields and bound the Hausdorff dimension of the set of ε-Dirichlet improvable vectors in this setting. This is a function field analogue of the results of Cheung and Chevallier [Duke Math.

arXiv (Cornell University), Mar 6, 2023

We show that there are infinitely many counterexamples to Minkowski's conjecture in positive char... more 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 radius, µ, by constructing a sequence of compact A orbits where µ obtains its conjectured upper bound. In addition, we show that these orbits, as well as a slightly larger sequence of orbits, must exhibit complete escape of mass.

arXiv (Cornell University), Aug 6, 2023

In this paper, we shall discuss topics in geometry of numbers in the positive characteristic sett... more In this paper, we shall discuss topics in geometry of numbers in the positive characteristic setting, such as covering radii. We find a closed form for covering radii with respect to convex bodies, which will lead to a proof of the positive characteristic analogue of Woods' conjecture in this setting. Then, we will prove a positive characteristic analogue of Minkowski's conjecture about the multiplicative covering radius. To do this, we shall prove a positive characteristic analogue of Solan's result that every diagonal orbit intersects the set of well rounded lattices. This implies that the Gruber-Mordell spectrum in positive characteristic is trivial in every dimension.

We show that there are infinitely many counterexamples to Minkowski's conjecture in positive char... more 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 radius, µ, by constructing a sequence of compact A orbits where µ obtains its conjectured upper bound. In addition, we show that these orbits, as well as a slightly larger sequence of orbits, must exhibit complete escape of mass.

arXiv (Cornell University), Mar 6, 2023

Deleted Journal, May 16, 2024

We show that there are infinitely many counterexamples to Minkowski's conjecture in posit... more 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 radius, µ, by constructing a sequence of compact A orbits where µ obtains its conjectured upper bound. In addition, we show that these orbits, as well as a slightly larger sequence of orbits, must exhibit complete escape of mass.

arXiv (Cornell University), May 18, 2024

We compute the Hausdorff dimension of the set of singular vectors in function fields and bound th... more We compute the Hausdorff dimension of the set of singular vectors in function fields and bound the Hausdorff dimension of the set of ε-Dirichlet improvable vectors in this setting. This is a function field analogue of the results of Cheung and Chevallier [Duke Math.

arXiv (Cornell University), Mar 6, 2023

We show that there are infinitely many counterexamples to Minkowski's conjecture in positive char... more 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 radius, µ, by constructing a sequence of compact A orbits where µ obtains its conjectured upper bound. In addition, we show that these orbits, as well as a slightly larger sequence of orbits, must exhibit complete escape of mass.

arXiv (Cornell University), Aug 6, 2023

In this paper, we shall discuss topics in geometry of numbers in the positive characteristic sett... more In this paper, we shall discuss topics in geometry of numbers in the positive characteristic setting, such as covering radii. We find a closed form for covering radii with respect to convex bodies, which will lead to a proof of the positive characteristic analogue of Woods' conjecture in this setting. Then, we will prove a positive characteristic analogue of Minkowski's conjecture about the multiplicative covering radius. To do this, we shall prove a positive characteristic analogue of Solan's result that every diagonal orbit intersects the set of well rounded lattices. This implies that the Gruber-Mordell spectrum in positive characteristic is trivial in every dimension.

We show that there are infinitely many counterexamples to Minkowski's conjecture in positive char... more 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 radius, µ, by constructing a sequence of compact A orbits where µ obtains its conjectured upper bound. In addition, we show that these orbits, as well as a slightly larger sequence of orbits, must exhibit complete escape of mass.

arXiv (Cornell University), Mar 6, 2023