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Bounds for GL3L-functions in depth aspect

  • Qingfeng Sun EMAIL logo and Rui Zhao
Published/Copyright: October 17, 2018

Abstract

Let f be a Hecke–Maass cusp form for SL3() and χ a primitive Dirichlet character of prime power conductor 𝔮=pκ, with p prime. We prove the subconvexity bound

L(12,πχ)p,π,ε𝔮3/4-3/40+ε

for any ε>0, where the dependence of the implied constant on p is explicit and polynomial.

MSC 2010: 11F66; 11F67; 11M41

Communicated by Freydoon Shahidi


Award Identifier / Grant number: 11871306

Award Identifier / Grant number: ZR2016AQ15

Award Identifier / Grant number: IRT16R43

Funding statement: The first author is supported by the National Natural Science Foundation of China (Grant No. 11871306), Natural Science Foundation of Shandong Province (Grant No. ZR2016AQ15) and PCSIRT (Grant No. IRT16R43).

Acknowledgements

The authors would like to express heartfelt thanks to the referees for their important and useful comments.

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Received: 2018-04-11
Revised: 2018-08-28
Published Online: 2018-10-17
Published in Print: 2019-03-01

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