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Shifted convolution sums for higher rank groups

  • Yujiao Jiang EMAIL logo and Guangshi Lü
Published/Copyright: October 16, 2018

Abstract

In this paper, we study some shifted convolution sums for higher rank groups. In particular, we establish an asymptotic formula for a GL(4)×GL(2) shifted convolution sum

nx|λf(n)|2rl(n+b),

where λf(n) are normalized Fourier coefficients of a Hecke holomorphic cusp form and rl(n) denotes the number of representations of n by the quadratic form x12++xl2.


Communicated by Freydoon Shahidi


Award Identifier / Grant number: 2017M620285

Award Identifier / Grant number: ZR2018QA004

Award Identifier / Grant number: 11801318

Award Identifier / Grant number: 11771252

Award Identifier / Grant number: 11531008

Award Identifier / Grant number: IRT16R43

Funding statement: Jiang is supported by the China Postdoctoral Science Foundation (no. 2017M620285), the Natural Science Foundation of Shandong Province (no. ZR2018QA004) and NSFC (no. 11801318), and Lü is supported in part by NSFC (nos. 11771252, 11531008), IRT16R43 and Taishan Scholars.

Acknowledgements

The authors wish to thank the referee for valuable comments.

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Received: 2017-12-31
Revised: 2018-09-07
Published Online: 2018-10-16
Published in Print: 2019-03-01

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