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Ikeda type lift on $\SO(3,n+1)$

Abstract

By using Ikeda's theory for a compatible family of Eisenstein series, we explicitly construct Ikeda type lifts on the special orthogonal group over with which splits everywhere at finite places. Our lifts are Hecke eigen cusp forms of weight (, even) and come from elliptic newforms with respect to which are of weight when is even and when is odd.