We shall introduce and study certain truncated sums of Hecke eigenvalues of $GL_2$-automorphic forms along quadratic polynomials. A power saving estimate is established and new applications to moments of critical $L$-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 details.
On the computation of coefficients of modular forms: the reduction modulo p approach
Benford's Law For Coefficients of Modular Forms and Partition Functions
Sign Changes of Coefficients and Sums of Coefficients of L-Functions
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