Temperedness of generic automorphic representations of exceptional groups
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Are all local components of globally generic cuspidal complex automorphic representations tempered for split connected adjoint absolutely simple groups of exceptional types G₂,F₄,E₆,E₇,E₈ over global function fields? The target includes ramified places and has no characteristic restriction.
Why it matters and what counts as progress
Why it matters: Every-place temperedness extends generic Ramanujan behavior to exceptional groups and arbitrarily ramified components.
What counts as progress: Prove temperedness at every place for these groups or remove restrictions in earlier generic Ramanujan results.
How the problem developed
- 6 Oct 2026 · Temperedness claim [1]
OpenAI Claimed that every local component of a globally generic cuspidal representation of a split connected adjoint exceptional group over a global function field is tempered, including ramified places and without a characteristic restriction.
AI contribution
Temperedness at ramified places for globally generic exceptional groups
For globally generic cuspidal complex automorphic representations of split connected adjoint absolutely simple groups of types G₂, F₄, E₆, E₇ or E₈ over global function fields, every local component is tempered, including arbitrarily ramified places and without a characteristic restriction.
Sources
Website timeline
Publication dates and editorial changes.
OpenAI reports temperedness at ramified exceptional-group places