Shifted convolution of cusp-forms with θ-series


DOI: 10.1007/s12188-010-0046-8

Cite this article as:
Luo, W. Abh. Math. Semin. Univ. Hambg. (2011) 81: 45. doi:10.1007/s12188-010-0046-8


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 convolutionTheta series and Poincare seriesCusp formVoronoi formula

Mathematics Subject Classification (2000)


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© Mathematisches Seminar der Universität Hamburg and Springer 2010

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA