Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 1759-1783 |
| Number of pages | 25 |
| Journal | Journal of the European Mathematical Society |
| Volume | 22 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2020 |
Bibliographical note
Publisher Copyright:© European Mathematical Society 2020
Keywords
- Automorphic L-functions
- Automorphic descents
- Bessel periods
- Central values
- Endoscopic classification of discrete spectrum
- Fourier coefficients of automorphic forms
- Unitary groups
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