Journal article
Improved subconvexity bounds for GL(2)xGL(3) and GL(3) L-functions by weighted stationary phase
Transactions of the American Mathematical Society, Vol.370(5), pp.3745-3769
2018
DOI: 10.1090/tran/7159
Abstract
Let f be a fixed self-contragradient Hecke–Maass form for SL(3, Z), and let u be an even Hecke–Maass form for SL(2, Z) with Laplace eigenvalue 1/4+k2, k ≥ 0. A subconvexity bound O((1+k)4/3+ε) in the eigenvalue aspect is proved for the central value at s = 1/2 of the Rankin–Selberg L-function L(s, f × u). Meanwhile, a subconvexity bound O((1 + |t|)2/3+ε) in the t aspect is proved for L(1/2+it, f). These bounds improved corresponding subconvexity bounds proved by Xiaoqing Li (Annals of Mathematics, 2011). The main techniques in the proofs, other than those used by Li, are nth-order asymptotic expansions of exponential integrals in the cases of the explicit first derivative test, the weighted first derivative test, and the weighted stationary phase integral, for arbitrary n ≥ 1. These asymptotic expansions sharpened the classical results for n = 1 by Huxley.
Details
- Title: Subtitle
- Improved subconvexity bounds for GL(2)xGL(3) and GL(3) L-functions by weighted stationary phase
- Creators
- Mark McKeeHaiwei SunYangbo Ye
- Resource Type
- Journal article
- Publication Details
- Transactions of the American Mathematical Society, Vol.370(5), pp.3745-3769
- DOI
- 10.1090/tran/7159
- ISSN
- 0002-9947
- eISSN
- 1088-6850
- Publisher
- American Mathematical Society; PROVIDENCE
- Grant note
- National Natural Science Foundation of China: 11601271 China Postdoctoral Science Foundation Funded Project: 2016M602125
The second author was partially supported by the National Natural Science Foundation of China (Grant No. 11601271) and China Postdoctoral Science Foundation Funded Project (Project No. 2016M602125).
- Language
- English
- Date published
- 2018
- Academic Unit
- Mathematics
- Record Identifier
- 9983985915702771
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