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arXiv · 0902.2496

A non-split sum of coefficients of modular forms

Nicolas Templier
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Abstract

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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Nicolas Templier. 2009-02-14. A non-split sum of coefficients of modular forms. https://doi.org/10.1215/00127094-2011-003

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