Improved Tail Estimates for the Distribution of Quadratic Weyl Sums

Francesco Cellarosi, Jory Griffin, Tariq Osman

We consider quadratic Weyl sums $S_N(x;c,\alpha )={\sum }_{n=1}^N\exp \{2\pi i((\frac{1}{2}{n}^2+cn)x+\alpha n)\}$ for $c=\alpha =0$ (the rational case) or $(c,\alpha )\notin {\mathbb{Q}}^2$ (the irrational case), wh…