On the Non-vanishing of the Central Value of Certain L-functions: Unitary Groups

2018/06/12 by Jiang, Dihua, Zhang, Lei · 1 citation
#11F66 #11F70 #22E55 #FOS: Mathematics #Number Theory (math.NT) #Primary 11F67 #Representation Theory (math.RT) #Secondary 11F30

paper · doi:10.48550/arxiv.1806.04340

Abstract

Let π be an irreducible cuspidal automorphic representation of a quasi-split unitary group \rm U_{\mathfrak n} 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 \rm U₁, for the case of \mathfrak n=2,3,4, and for the general \mathfrak n≥ 5 by assuming a conjecture 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.

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