The spectral decomposition of shifted convolution sums

@article{Blomer2007TheSD,
  title={The spectral decomposition of shifted convolution sums},
  author={Valentin Blomer and Gergely Harcos},
  journal={Duke Mathematical Journal},
  year={2007},
  volume={144},
  pages={321-339}
}
Let pi(1), pi(2)) be cuspidal automorphic representations of PGL(2)(R) Qf conductor 1 and Hecke eigenvalues lambda(pi 1,2) (n) and let h > 0 be an integer. For any smooth compactly supported weight functions W-1,W-2 : R-x --> C and any Y > 0, aspectral decomposition of the shifted convolution sum Sigma(m+/-n=h) lambda(pi 1) (vertical bar m vertical bar)lambda(pi 2) (vertical bar n vertical bar)/root vertical bar mn vertical bar W-1(m/Y)W-2(n/Y) is obtained. As an application, aspectral… 
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