Shifted convolution sums for $GL(3)\times GL(2)$

Abstract

For the shifted convolution sum $$D_h(X)=\sum _{m=1}^{\infty }{\lambda }_1(1,m){\lambda }_2(m+h)V(\frac{m}{X})$$ where ${\lambda }_1(1,m)$ are the Fourier coefficients of a $SL(3,\mathbb{Z})$ Maass form ${\pi }_1$, and ${\lambda }_2(m)$ are those of a $SL(2,\mathbb{Z})$ Maass or holomorphic form ${\pi }_2$, and $1\le |h|\ll X^{1+\epsilon }$, we establish the bound $$D_h(X){\ll }_{{\pi }_1,{\pi }_2,\epsilon }{X}^{1-(1/20)+\epsilon }.$$ The bound is uniform with respect to the shift $h$.

References in corpus (3)

• The spectral decomposition of shifted convolution sums
• An additive problem in the Fourier coefficients of cusp forms
• Level Aspect Subconvexity For Rankin-Selberg $L$-functions

Cited by in corpus (3)

• A study in sums of products
• The Voronoi formula and double Dirichlet series
• Shifted convolution sum with weighted average : $GL(3)\times GL(3)$ setup