Abstract
Let f be a Hecke-Maass cusp form for SL(3,ℤ) with Fourier coeffcients Af (m, n), and let ϕ(x) be a C∞-function supported on [1, 2] with derivatives bounded by ϕ(j)(x)≪j 1: We prove an asymptotic formula for the nonlinear \(\Sigma_{n\equiv l \rm{mod} \it{q}}\)Af (m, n)ϕ(n/X)e(3(kn)1/3/q), where e(z) = e2πiz and k ∈ℤ+.
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The author would like to thank Professor Qingfeng Sun for his valuable advice and constant encouragement.
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He, X. Exponential sums involving automorphic forms for GL(3) over arithmetic progressions. Front. Math. China 13, 1355–1368 (2018). https://doi.org/10.1007/s11464-018-0732-x
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DOI: https://doi.org/10.1007/s11464-018-0732-x