Isolation of the cuspidal spectrum:The function field case
Isolation of the cuspidal spectrum:The function field case
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DOI：
10.1007/s11425-020-1851-y
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Xu Bin
中科院分区：
文献类型：
--
作者：
Cai Li;Xu Bin
Isolating cuspidal automorphic representations from the whole automorphic spectrum is a basic problem in the trace formula approach.For example,matrix coefficients of supercuspidal representations can be used as test functions for this.However,they kill a large class of interesting cuspidal automorphic representations.For the case of number fields,multipliers of the Schwartz algebra are used in the recent work (see Beuzart-Plessis et al.(2021)) to isolate all the cuspidal spectrum.In particular,they are suitable for the comparison of orbital integrals.These multipliers are then applied to the proof of the Gan-Gross-Prasad conjecture for unitary groups (see Beuzart-Plessis et al.(2021,2022)).In this article,we prove the similar result on isolating the cuspidal spectrum in Beuzart-Plessis et al.(2021) for the function field case.
