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A note on shifted convolution of cusp-forms with \(\theta \)-series

  • Xiaoguang He
  • Yujiao Jiang
Article
  • 33 Downloads

Abstract

In this paper, we study shifted convolution sums for GL(2) and give an upper bound for \(\sum \nolimits _{n\ge 1}\lambda _f(n+b) r(n,Q)g(n)\), where g(n) is a smooth weight function. In particular, we get an upper bound for \(\sum \nolimits _{n\le x}\lambda _f(n+b)r_3(n)\), which improves the result in Lü et al. (Ramanujan J 40(1):C115–C133, 2016).

Keywords

Shifted convolution sum Cusp forms Theta series 

Mathematics Subject Classification

11F30 11F11 11F27 11F37 

Notes

Acknowledgements

The authors are very grateful to the referee for thorough reading of the paper and many valuable suggestions that clarify the argument of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShandong UniversityJinanChina
  2. 2.School of Mathematics and StatisticsShandong UniversityWeihaiChina

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