A nonsplit sum of coefficients of modular forms

Templier, Nicolas

Duke Math. J., Tome 156 (2011) no. 1, p. 109-165 / Harvested from Project Euclid

Résumé

We introduce and study certain truncated sums of Hecke eigenvalues of ${\rm GL}_2$ -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 detail.

Publié le : 2011-03-15
Classification: 11L07, 11F30

@article{1300281534,
     author = {Templier, Nicolas},
     title = {A nonsplit sum of coefficients of modular forms},
     journal = {Duke Math. J.},
     volume = {156},
     number = {1},
     year = {2011},
     pages = { 109-165},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1300281534}
}

Templier, Nicolas. A nonsplit sum of coefficients of modular forms. Duke Math. J., Tome 156 (2011) no. 1, pp.  109-165. http://gdmltest.u-ga.fr/item/1300281534/