In the paper, we prove the local Gan-Gross-Prasad conjecture for special orthogonal groups over archimedean local fields for generic local $L$-parameters. The non-archimedean case was proved by C. Moeglin and J.-L. Waldspurger in \cite{moeglin2012conjecture}. When the local $L$-parameters are tempered, the conjecture was proved by Waldspurger in \cite{waldspurger2009conjecture} for non-archimedean local fields and by Zhilin Luo in \cite{luo2020local} for archimedean local fields.
The local theta correspondence and the local Gan-Gross-Prasad conjecture for the symplectic-metaplectic case
Local Zeta Functions, pseudodifferential operators, and Sobolev-type spaces over non-Archimedean Local Fields
Explicit formula for generalization of Poly-Bernoulli numbers and polynomials with a,b,c parameters
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