On the local factors of representations of classical groups

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The Gross–Prasad conjecture and local theta correspondence (2014, methodology): “To show that Π′ is nonzero, we consider the standard L-function L(s,Π) of Π defined using the doubling zeta integral of Piatetski-Shapiro–Rallis [30], [26].”
A Refined Gross-Prasad Conjecture for Unitary Groups (2012, methodology): “Now we use the result in [24] to obtain the claim at the beginning of the proof.”
Formal degrees and local theta correspondence (2013, methodology): “2, we have recalled the normalization of the intertwining operator M(s,χ) due to Lapid-Rallis [50].”
L-functions and theta correspondence for classical groups (2014, methodology): “To begin, we record necessary results included in [32] (see also [4]).”
The Iwasawa Main Conjectures for GL2 (2014, background): “which in the notation of [LR05] is Z(M(z)fz, φ ′ 1 ⊗ φ) (with V = (V1, w1)).”
Doubling constructions and tensor product L-functions: the linear case (2017, unknown): “Interestingly, the odd orthogonal case was excluded from [67] and was first treated only in [62] (for technical reasons).”