Shifted convolution of cusp-forms with θ-series



We generalize the classical Voronoi formula for
$$r_{l}(n) = \#\{ (n_{1}, \ldots , n_{l}) \in \mathbf{Z}^{l}, n_{1}^{2} + \cdots + n_{l}^{2} = n \},$$
and as an application, we derive a sharp bound for the shifted convolution sum convolving the Fourier coefficients of holomorphic cusp forms with those of theta series.


Shifted convolution Theta series and Poincare series Cusp form Voronoi formula 

Mathematics Subject Classification (2000)

11F11 11F27 11F30 11F37 


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© Mathematisches Seminar der Universität Hamburg and Springer 2010

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

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