Sums of Hecke eigenvalues over quadratic polynomials

dc.creatorBlomer, Valentin
dc.date2008-03-30
dc.date.accessioned2026-07-07T09:29:21Z
dc.date.available2026-07-07T09:29:21Z
dc.descriptionLet f(z) = sum_n a(n) n^{(k-1)/2} e(nz) be a cusp form for Gamma_0(N), character chi and weight k geq 4. Let q(x) = x^2 + sx + t be a polynomial with integral coefficients. It is shown that sum_{n \leq X} a(q(n)) = cX + O(X^{6/7+eps}) for some constant c depending on f and q. The constant vanishes in many cases, for example if k is even. On the way a Kuznetsov formula for half-integral weight and entries having different sign is derived.
dc.description22 pages
dc.identifierhttps://arxiv.org/abs/0803.4301
dc.identifierhttp://arxiv.org/abs/0803.4301
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/157751
dc.subjectNumber Theory
dc.subject11F30, 11F37, 11N37
dc.titleSums of Hecke eigenvalues over quadratic polynomials
dc.typetext

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