Shifted convolution of cusp-forms with θ-series

Abstract : In this paper we apply simple approachs to improve a recent result due to Luo, concerning a shifted convolution sum involving the Fourier coefficients of cusp forms with those of theta series. In order to explore what should be the best possible bound, a mean square result of this shifted convolution sum is also established.
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Guangshi Lu, Jie Wu, Wenguang Zhai. Shifted convolution of cusp-forms with θ-series. Ramanujan Journal (The), 2016, 40 (1), pp.115-133. ⟨10.1007/s11139-015-9678-8⟩. ⟨hal-01313346⟩

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