Sums of Fourier coefficients involving theta series and Dirichlet characters

Yanxue Yu

Let $f$ be a holomorphic or Maass cusp forms for $\mathrm{S}{\mathrm{L}}_2(\mathbb{Z})$ with normalized Fourier coefficients ${\lambda }_f(n)$ and \bna r_{\ell}(n)=\#\left\{(n_1,\cdots,n_{\ell})\in \mathb…