English

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

Number Theory 2019-12-19 v1

Abstract

For the shifted convolution sum Dh(X)=m=1λ1(1,m)λ2(m+h)V(mX) D_h(X)=\sum_{m=1}^\infty\lambda_1(1,m)\lambda_2(m+h)V(\frac{m}{X}) where λ1(1,m)\lambda_1(1,m) are the Fourier coefficients of a SL(3,Z)SL(3,\mathbb Z) Maass form π1\pi_1, and λ2(m)\lambda_2(m) are those of a SL(2,Z)SL(2,\mathbb Z) Maass or holomorphic form π2\pi_2, and 1hX1+ε1\leq |h| \ll X^{1+\varepsilon}, we establish the bound Dh(X)π1,π2,εX1(1/20)+ε. D_h(X)\ll_{\pi_1,\pi_2,\varepsilon} X^{1-(1/20)+\varepsilon}. The bound is uniform with respect to the shift hh.

Keywords

Cite

@article{arxiv.1202.1157,
  title  = {Shifted convolution sums for $GL(3)\times GL(2)$},
  author = {Ritabrata Munshi},
  journal= {arXiv preprint arXiv:1202.1157},
  year   = {2019}
}
R2 v1 2026-06-21T20:15:26.783Z