Abstract. We relate poles of local Godement-Jacquet L-functions to distributions on matrix spaces with singular supports. As an application, we show the irreducibility of the full theta lifts to GL n (F) of generic irreducible representations of GL n (F), where F is an arbitrary local field.
Abstract. Inspired by Sun's breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups GL n (R)×GL n−1 (R) and GL n (C) × GL n−1 (C), we confirm it for GL n (C) × GL n (C) at the central critical point.
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