The authors prove three families of non-tempered cases of the global Gan-Gross-Prasad conjecture by relating special periods to L-values through theta-lift genericity and Rankin-Selberg integrals.
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First occurrence of global theta lifts preserves genericity, applied to prove the global Gan-Gross-Prasad conjecture for SO(2n+1) × SO(2) when SO(2) is split and the representation is trivial.
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Special periods and some non-tempered cases of the Gan-Gross-Prasad conjecture
The authors prove three families of non-tempered cases of the global Gan-Gross-Prasad conjecture by relating special periods to L-values through theta-lift genericity and Rankin-Selberg integrals.
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The tower property on the genericity of global theta lifts
First occurrence of global theta lifts preserves genericity, applied to prove the global Gan-Gross-Prasad conjecture for SO(2n+1) × SO(2) when SO(2) is split and the representation is trivial.