Improved tail estimates for the distribution of quadratic Weyl sums (Q6104263)

Techniques for tail estimates (that is, the asymptotic probability of falling outside a ball of radius \(R\)) for normalized Weyl sums of the form \[ (1/\sqrt{N})\sum_{n=1}^{N}\exp \bigl(2\pi{\mathrm{i}}((n^2/2+cn)x+\alpha n)\bigr) \] obtained by \textit{F. Cellarosi} and \textit{J. Marklof} [Proc. Lond. Math. Soc. (3) 113, No. 6, 775--828 (2016; Zbl 1423.11145)] are refined to improve the estimates.