We introduce and study certain truncated sums of Hecke eigenvalues of -automorphic forms along quadratic polynomials. A power-saving estimate is established, and new applications to moments of critical -values associated to quadratic fields are derived. An application to the asymptotic behavior of the height of Heegner points and singular moduli is discussed in detail.
"A nonsplit sum of coefficients of modular forms." Duke Math. J. 157 (1) 109 - 165, 15 March 2011. https://doi.org/10.1215/00127094-2011-003