On a Conjecture of Jacquet
نویسندگان
چکیده
In a previous paper [4], we proved this conjecture in the special case where k = Q and the πi’s correspond to a triple of holomorphic newforms. Our method was based on a combination of the Garrett, Piatetski-Shapiro, Rallis integral representation of the triple product L-function with the extended Siegel–Weil formula and the seesaw identity. The restriction to holomorphic newforms over Q arose from (i) the need to invoke the Ramanujan Conjecture to control the poles of some bad local factors and (ii) the use of a version of the Siegel–Weil formula for similitudes. In this note, we show that, thanks to the recent improvement on the Ramanujan bound due to Kim–Shahidi [11], together with a slight variation in the setup of (ii), our method yields Jacquet’s conjecture in general.
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