The generalized Ramanujan conjecture for globally generic cuspidal representations of exceptional groups over function fields
Theorem 1.1: for split connected adjoint absolutely simple of type or over a global function field, every complex globally generic cuspidal automorphic representation is tempered at every place. The companion (September 24) gives temperedness at unramified places for all split adjoint absolutely simple groups from genericity at one unramified place. Nothing is claimed over number fields, for non-generic representations, or for ramified places of classical groups beyond what Lomeli already proved.
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Occurred: Oct 5, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The generalized Ramanujan conjecture for globally generic cuspidal representations of exceptional groups over function fields · Generic Ramanujan, exceptional groups, F_q(X)
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
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The generalized Ramanujan conjecture for globally generic cuspidal representations of exceptional groups over function fields parent of this event
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VibeMathed record: The generalized Ramanujan conjecture for globally generic cuspidal representations of exceptional groups over function fields evidence for this event
Theorem 1.1: for split connected adjoint absolutely simple of type or over a global function field, every complex globally generic cuspidal automorphic representation is tempered at every place. The companion (September 24) gives temperedness at unramified places for all split adjoint absolutely simple groups from genericity at one unramified place. Nothing is claimed over number fields, for non-generic representations, or for ramified places of classical groups beyond what Lomeli already proved. parent of this event
Companion: Ramanujan-Arthur Decompositions of Cuspidal Functions at Full Finite Level evidence for this event
The generalized Ramanujan conjecture for globally generic cuspidal representations of exceptional groups over function fields evidence for this event
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