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Cancellation in algebraic twisted sums on GL_m

  • Yujiao Jiang and Guangshi Lü EMAIL logo
Published/Copyright: June 30, 2021

Abstract

Let π be an automorphic irreducible cuspidal representation of GLm over with unitary central character, and let λπ(n) be its n-th Dirichlet series coefficient. We study short sums of isotypic trace functions associated to some sheaves modulo primes q of bounded conductor, twisted by multiplicative functions λπ(n) and μ(n)λπ(n). We are able to establish non-trivial bounds for these algebraic twisted sums with intervals of length of at least q1/2+ε for an arbitrary fixed ε>0.


Communicated by Freydoon Shahidi


Award Identifier / Grant number: 11801318

Award Identifier / Grant number: 11771252

Award Identifier / Grant number: 12031008

Award Identifier / Grant number: ZR2018QA004

Award Identifier / Grant number: IRT16R43

Funding statement: Y. Jiang is supported by the Natural Science Foundation of Shandong Province (No. ZR2018QA004) and NSFC (No. 11801318). G. Lü is supported in part by NSFC (Nos. 11771252, 12031008), IRT16R43, and Taishan Scholars.

Acknowledgements

The authors are very grateful to the referee for valuable and detailed comments.

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Received: 2020-09-08
Revised: 2021-03-25
Published Online: 2021-06-30
Published in Print: 2021-07-01

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