Let π be an irreducible cuspidal automorphic representation of a quasisplit unitary group Un defined over a number field F. Under the assumption that π has a generic global Arthur parameter, we establish the non-vanishing of the central value of L-functions, L(1/2, π × χ), with a certain automorphic character χ of U1, for the case of n = 2, 3, 4, and for the general n ≥ 5 by assuming Conjecture 1.4 on certain refined properties of global Arthur packets. In consequence, we obtain some simultaneous non-vanishing results for the central L-values by means of the theory of endoscopy.
Bibliographical noteFunding Information:
The research of the first named author is supported in part by the NSF DMS-1600685 and DMS-1901802, and that of the second named author is supported in part by the start-up grant, AcRF Tier 1 grants R-146-000-237-114 and R-146-000-277-114 of National University of Singapore.
© European Mathematical Society 2020
- Automorphic L-functions
- Automorphic descents
- Bessel periods
- Central values
- Endoscopic classification of discrete spectrum
- Fourier coefficients of automorphic forms
- Unitary groups