Shifted convolution of cusp-forms with θ-series

Article

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

Abstract

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.

Keywords

Shifted convolution Theta series and Poincare series Cusp form Voronoi formula 

Mathematics Subject Classification (2000)

11F11 11F27 11F30 11F37 

Copyright information

© Mathematisches Seminar der Universität Hamburg and Springer 2010

Authors and Affiliations

  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

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