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Frontiers of Mathematics in China

, Volume 13, Issue 6, pp 1355–1368 | Cite as

Exponential sums involving automorphic forms for GL(3) over arithmetic progressions

  • Xiaoguang HeEmail author
Research Article
  • 10 Downloads

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+.

Keywords

Automorphic forms for GL(3) exponential sum arithmetic progression 

MSC

11L05 11L07 11F30 

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Notes

Acknowledgements

The author would like to thank Professor Qingfeng Sun for his valuable advice and constant encouragement.

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina

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