Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 81, Issue 1, pp 45–53

Shifted convolution of cusp-forms with θ-series


    • Department of MathematicsThe Ohio State University

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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