Analytic Twists of GL3 × GL2 Automorphic Forms

@article{Lin2021AnalyticTO,
  title={Analytic Twists of GL3 × GL2 Automorphic Forms},
  author={Yongxiao Lin and Qingfeng Sun},
  journal={International Mathematics Research Notices},
  year={2021}
}
Let $\pi $ be a Hecke–Maass cusp form for $\textrm{SL}_3(\mathbb{Z})$ with normalized Hecke eigenvalues $\lambda _{\pi }(n,r)$. Let $f$ be a holomorphic or Maass cusp form for $\textrm{SL}_2(\mathbb{Z})$ with normalized Hecke eigenvalues $\lambda _f(n)$. In this paper, we are concerned with obtaining nontrivial estimates for the sum $$\begin{align*}& \sum_{r,n\geq 1}\lambda_{\pi}(n,r)\lambda_f(n)e\left(t\,\varphi(r^2n/N)\right)V\left(r^2n/N\right), \end{align*}$$where $e(x)=e^{2\pi ix}$, $V(x… 
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