A non-split sum of coefficients of modular forms

Details A non-split sum of coefficients of modular forms A non-split sum of coefficients of modular forms

2009-02-14

arxiv.org/abs/0902.2496v1

Mathematics

Number Theory

Scientific paper

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.

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