Non-split Sums of Coefficients of GL(2)-Automorphic Forms

Nicolas Templier, Jacob Tsimerman

Given a cuspidal automorphic form $\pi$ on $\GL_2$, we study smoothed sums of the form ${\sum }_{n\in \mathbb{N}}{a}_{\pi }(n^2+d)W(\frac{n}{Y})$. The error term we get is sharp in that it is…