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International Mathematics Research Notices (2008) Vol. 2008 : article ID rnn059, 29 pages, doi:10.1093/imrn/rnn059 published on June 13, 2008
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© The Author 2008. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org

Sums of Hecke Eigenvalues over Values of Quadratic Polynomials

Valentin Blomer

Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, M5S 2E4, Canada

Correspondence: Correspondence to be sent to: vblomer{at}math.toronto.edu

Let Formula be a cusp form for {Gamma}0(N), weight k ≥ 4, and character {chi}. Let Formula be a quadratic polynomial. It is shown that


Formula 1

for some constant c = c(f, q). The constant vanishes in many (but not all) cases, for example, if k is even or if {Delta} = s2 – 4t > 0. On the way, a Kuznetsov formula for half-integral weight and entries having different sign is derived.


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