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).
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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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This work was supported by Shandong Province Natural Science Foundation (Grant No. ZR2016AP03).
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He, X., Jiang, Y. A note on shifted convolution of cusp-forms with \(\theta \)-series. Ramanujan J 47, 1–19 (2018). https://doi.org/10.1007/s11139-018-0018-7
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DOI: https://doi.org/10.1007/s11139-018-0018-7