Hsieh M.-LYamana S.MING-LUN HSIEH2022-11-112022-11-11202210884165https://www.scopus.com/inward/record.uri?eid=2-s2.0-85129904497&doi=10.1090%2fERT%2f602&partnerID=40&md5=16c056f55ac2c002f41667c083861f6bhttps://scholars.lib.ntu.edu.tw/handle/123456789/624830Abstract. Let πi be an irreducible cuspidal automorphic representation of GL2 with central character ωi. When ω1ω2ω3 is trivial, Atsushi Ichino proved a formula for the central value (Formula Presented) of the triple product L-series in terms of global trilinear forms. We will extend this formula to the case when ω1ω2ω3 is a quadratic character, giving a non-vanishing criterion of a local trilinear form in terms of the central value of the gamma factor. © 2022. American Mathematical Societyjournal article10.1090/ERT/6022-s2.0-85129904497