On Local L-Functions and Normalized Intertwining Operators

By Henry H. Kim. Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2005

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A Refined Gross-Prasad Conjecture for Unitary Groups (2012, background): “Using the Ramanujan bounds from [21] and [22] obviates this assumption.”
Functoriality for the quasisplit classical groups (2011, result): “Note that in view of the results of Mui´c [34] and of [8], the necessary result on normalized intertwining operators, Assumption 1.1 of [28], usually referred to as Assumption A [24], is valid in all cases as proved in [24, 25 ].”
On endoscopy and the refined Gross–Prasad conjecture for (SO5, SO4) (2010, unknown): “By the Kim–Shahidi estimate [26,28], there exist (7)9 < λ1, λ2, λ3, λ4 1 such that |Bτ (τ(t(a1, a2))f1, f2)| C|a1| |a2| , |Bσ(σ(t(a3, a4))φ1, φ2)| C|a3| |a4| , for a1, a2, a3, a4 ∈ F+ with some constant C.”
Functoriality for the classical groups (2004, methodology): “Note that in view of the results of Mui´ c [44] and of [4], the necessary result on normalized intertwining operators, Assumption 1.1 of [32], usually referred to as Assumption A [28], is valid in all cases as proved in [28, 31 ].”