Sums of Cusp Form Coefficients Along Quadratic Sequences

Chan Ieong Kuan, David Lowry-Duda, Alexander Walker +1

Let $f(z)=\sum A(n)n^{(k-1)/2}e(nz)$ be a cusp form of weight $k\ge 3$ on ${\Gamma }_0(N)$ with character $\chi$. By studying a certain shifted convolution sum, we prove that $\sum_{n \…