A non-split sum of coefficients of modular forms
Abstract
We shall introduce and study certain truncated sums of Hecke eigenvalues of GL2-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.
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