Tariq Osman

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20222024

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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…