Shifted convolution of cusp-forms with θ-series

Guangshi Lu (1) , Jie Wu (2) , Wenguang Zhai (3)

1 School of Mathematics [Shandong]
2 IECL - Institut Élie Cartan de Lorraine
3 CUMT - China University of Mining and Technology

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.

Domaines: Théorie des nombres [math.NT]

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⟩