Nattalie Tamam

activity

20122024

most citedHausdorff dimension of weighted singular vectors

1 citations · 1 across the 9 of their papers we have counts for

collaborators

10 papers

math.NT2024

On weighted singular vectors for multiple weights

Shreyasi Datta, Nattalie Tamam

We introduce the notion of weighted singular vectors and weighted uniform exponent with respect to a set of weights. We prove invariance of these exponents for affine subspaces and…

math.DS2022

Geometric interpretation of quantitative instability

Omri N. Solan, Nattalie Tamam

Given a real algebraic group $G$ acting on a linear space $V$ , a vector $v \in V$ is called unstable if $0 \in G v - G v$ , where the closure is taken with respect to the Zaris…

math.NT2022

Property tau in positive characteristic

Amir Mohammadi, Nattalie Tamam

We prove a quantitative equidistribution statement for certain adelic homogeneous subsets in positive characteristic. As an application, we describe a proof of property tau for ari…

math.DS2022

On Topologically Big Divergent Trajectories

Omri N. Solan, Nattalie Tamam

We study the behavior of $A$ -orbits in $G /Γ$ , when $G$ is a semisimple real algebraic $Q$ -group, $Γ$ is a non-uniform arithmetic lattice, and $A$ is a torus of dimension $…

math.DS2020

Distribution of orbits of geometrically finite groups acting on null vectors

Nattalie Tamam, Jacqueline M. Warren

We study the distribution of non-discrete orbits of geometrically finite groups in $SO (n, 1)$ acting on $R^{n + 1}$ , and more generally on the quotient of $\op…

math.DS2020

Effective equidistribution of horospherical flows in infinite volume rank one homogeneous spaces

Nattalie Tamam, Jacqueline M. Warren

We prove effective equidistribution of horospherical flows in $SO (n, 1)^{\circ} /Γ$ when $Γ$ is geometrically finite and the frame flow is exponentially mixing for the…

math.DS2019

Existence of Non-Obvious Divergent Trajectories in homogeneous spaces

Nattalie Tamam

We prove a modified version for a conjecture of Weiss from 2004. Let $G$ be a semisimple real algebraic group defined over $Q$ , $Γ$ be an arithmetic subgroup of $G$ . A tra…

math.DS2018

Divergent Trajectories in Arithmetic Homogeneous Spaces of Rational Rank Two

Nattalie Tamam

Let $G$ be a real algebraic group defined over $Q$ , $Γ$ be an arithmetic subgroup of $G$ , and $T$ be a maximal $R$ -split torus. A trajectory in $G /Γ$ is divergent…

math.DS2016★ 1 cited

Hausdorff dimension of weighted singular vectors

Lingmin Liao, Ronggang Shi, Omri N. Solan +1

Let $w = (w_{1}, w_{2})$ be a pair of positive real numbers with $w_{1} + w_{2} = 1$ and $w_{1} \geq w_{2}$ . We show that the set of $w$ -weighted singular vectors in $R^{2}$ has Hausdorff dimens…

math.NT2012

The Fourth Moment of Dirichlet L-Functions for the Rational Function Field

Nattalie Tamam

We study the moments of the Dirichlet L-function when defined over the polynomial ring over finite fields. We find an asymptotic formula to the fourth moment of the central value o…