A non-split sum of coefficients of modular forms

Abstract

We shall introduce and study certain truncated sums of Hecke eigenvalues of $G{L}_2$-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.

References in corpus (1)

• Uniform approximate functional equation for principal L-functions

Cited by in corpus (3)

• Subconvexity and equidistribution of Heegner points in the level aspect
• Wide moments of $L$-functions I: Twists by class group characters of imaginary quadratic fields
• Sum of the $GL(3)$ Fourier coefficients over quadratics