Hardy-Littlewood series and even continued fractions

Tanguy Rivoal, Stéphane Seuret

For any $s\in (1/2,1]$, the series$F_s(x)={\sum }_{n=1}^{\infty }{e}^{i\pi n^{2}x}/n^s$ converges almost everywhere on $[-1,1]$ by a result of Hardy-Littlewood, but not everywhere. However,…