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.
The Langlands-Shahidi method over function fields: Ramanujan Conjecture and Riemann Hypothesis for the unitary groups
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abstract
We establish the Langlands-Shahidi method over a global field of characteristic p. We then focus on the unitary groups and prove global and local Langlands functoriality to general linear groups for generic representations. Main applications are to the Ramanujan Conjecture and Riemann Hypothesis.
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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.