Shifted convolution sums of GL₃ cusp forms with θ-series

2015/09/25 by Sun, Qingfeng
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1509.07644

Abstract

Let A_f(1,n) be the normalized Fourier coefficients of a Hecke-Maass cusp form f for SL₃(ℤ) and r₃(n)=#\(n₁,n₂,n₃)∈ ℤ³:n₁²+n₂²+n₃²=n\. Let 1≤ h≤ X and ϕ(x) be a smooth function compactly supported on [1/2,1]. It is shown that ∑_{n≥ 1}A_f(1,n+h)r₃(n)ϕ((n)/(X)) ≪_f,ε X^{(3)/(2)-(1)/(8)+ε} uniformly with respect to the shift h.

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