I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level G(Ẑ) and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U1 × U1 × U1 and U1 × U2, and to an example of a non-endoscopic f...

Abstract Lapid and Mao formulated a conjecture on an explicit formula of Whittaker–Fourier coefficients automorphic forms quasi-split reductive groups metaplectic as analogue the Ichino–Ikeda conjecture. They also showed that this is reduced to certain local identity in case unitary groups. In article, we study even unitary-group case. Indeed, prove over p -adic fields. Further, equivalence bet...

‎We first give bounds for domains where the unitarizabile subquotients can show up in the parabolically induced representations of classical $p$-adic groups‎. ‎Roughly‎, ‎they can show up only if the‎ ‎central character of the inducing irreducible cuspidal representation is dominated by the‎ ‎square root of the modular character of the minimal parabolic subgroup‎. ‎For unitarizable subquotients...