{"id":"openai-math/Temperedness-at-ramified-places-for-globally-generic-exceptional-groups","pdf":"https://github.com/openai/math/blob/main/preprints/Temperedness-at-ramified-places-for-globally-generic-exceptional-groups-October-5-2026/ramified-ramanujan.pdf","url":"https://github.com/openai/math/tree/main/preprints/Temperedness-at-ramified-places-for-globally-generic-exceptional-groups-October-5-2026","tags":["automorphic-forms","ramanujan-conjecture","exceptional-groups"],"score":0,"title":"Temperedness at ramified places for globally generic exceptional groups","domain":"Number theory","family":"014","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.NT","summary":"We prove the generalized Ramanujan conjecture for globally generic cuspidal automorphic representations of split connected adjoint exceptional groups over global function fields. Every local component is tempered, without restrictions on characteristic or ramification depth. The proof extends the unramified Ramanujan theorem of a companion paper to all ramified places.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"Restricted geometric Langlands, global Arthur enhancements, and generic Ramanujan"}