Local $L^2$-regularity of Riemann's Fourier series

Stéphane Seuret, Adrián Ubis

We are interested in the convergence and the local regularity of the lacunary Fourier series $F_s(x)={\sum }_{n=1}^{+\infty }\frac{e^{2i\pi n^{2}x}}{n^s}$. In the 1850's, Riemann introd…