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Canadian Number Theory Association X Meeting (CNTA X)
July 13-18, 2008
University of Waterloo
Waterloo, Ontario, Canada

Organizers
Kevin Hare (Waterloo, Wentang Kuo (Waterloo), Yu-Ru Liu (Waterloo), David McKinnon (Waterloo), Michael Rubinstein (Waterloo), Cam Stewart (Waterloo)

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Sums of Hecke eigenvalues over quadratic polynomials
by
Valentin Blomer
University of Toronto

Let a(n) be the normalized Fourier coefficients of a modular form f ∈ Sk(N, c), and let q(x) = x2+sx+t be an integral quadratic polynomial. It is shown that

å
n ≤ X 
 a(q(n)) = cX + O(X6/7+e)
for some constant c = c(f, q). The constant vanishes in many, but not all, cases.

Date received: April 21, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawl-28.