Tariq Osman

activity

20222024

collaborators

4 papers

math.DS2024

An Effective Slope Gap Distribution for Lattice Surfaces

Tariq Osman, Joshua Southerland, Jane Wang

We prove an effective slope gap distribution result first for the square torus and then for general lattice translation surfaces. As a corollary, we obtain a dynamical proof for an…

math.NT2023

Bounds for Smooth Theta Sums with Rational Parameters

Francesco Cellarosi, Tariq Osman

We provide an explicit family of pairs $(α, β) \in R^{k} \times R^{k}$ such that for sufficiently regular $f$ , there is a constant $C > 0$ for which the theta sum bound…

math.NT2022

Heavy tailed and compactly supported distributions of quadratic Weyl sums with rational parameters

Francesco Cellarosi, Tariq Osman

We consider quadratic Weyl sums $S_{N} (x; α, β) = \sum_{n = 1}^{N} exp [2 π i ((\frac{1}{2} n^{2} + β n) x + α n)]$ for $(α, β) \in Q^{2}$ , where $x\in\mathbb{R…

math.NT2022

Improved Tail Estimates for the Distribution of Quadratic Weyl Sums

Francesco Cellarosi, Jory Griffin, Tariq Osman

We consider quadratic Weyl sums $S_{N} (x; c, α) = \sum_{n = 1}^{N} exp {2 π i ((\frac{1}{2} n^{2} + c n) x + α n)}$ for $c = α = 0$ (the rational case) or $(c, α) \in / Q^{2}$ (the irrational case), wh…