Hölder regularity of arithmetic Fourier series arising from modular forms

Izabela Petrykiewicz

Given a modular form which is not a cusp form $M_k(z)={\sum }_{n=0}^{\infty }{r}_n{e}^{2\pi inz}$ of weight $k\ge 4$, we define the series $M_{k,s}(x)=\sum_{n=1}^{\infty}\frac{r_n}{n^s}\sin…