Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg

, Volume 81, Issue 1, pp 45-53

First online:

Shifted convolution of cusp-forms with θ-series

  • Wenzhi LuoAffiliated withDepartment of Mathematics, The Ohio State University Email author 

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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