Differentiability of arithmetic Fourier series arising from Eisenstein series

Izabela Petrykiewicz

Let $k$ be even. We consider two series $F_k(x)={\sum }_{n=1}^{\infty }\frac{{\sigma }_{k-1}(n)}{n^{k+1}}\sin (2\pi nx)$ and $G_k(x)={\sum }_{n=1}^{\infty }\frac{{\sigma }_{k-1}(n)}{n^{k+1}}\cos (2\pi nx)$, w…