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Number Theory Seminar
Seminar information archive ～05/17｜Next seminar｜Future seminars 05/18～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Naoki Imai, Shane Kelly |
2026/07/01
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
ISHIKURA Rintaro (University of Tokyo)
On boundedness of the number of cuspidal automorphic representations of Mp(4) ordinary at p
ISHIKURA Rintaro (University of Tokyo)
On boundedness of the number of cuspidal automorphic representations of Mp(4) ordinary at p
[ Abstract ]
We study p-ordinary cuspidal automorphic representations of the metaplectic group Mp(4) with holomorphic discrete series at infinity, whose A-parameters are tempered. Using two Iwahori-level Hecke operators, we define an ordinary projector and investigate the conditions to be ordinary at p. Fixing the level K, we prove a bound (depending only on K) for the number of genuine cuspidal automorphic representations of Mp(4) ordinary at p and containing nonzero K-fixed vectors, as the holomorphic weight varies.
We study p-ordinary cuspidal automorphic representations of the metaplectic group Mp(4) with holomorphic discrete series at infinity, whose A-parameters are tempered. Using two Iwahori-level Hecke operators, we define an ordinary projector and investigate the conditions to be ordinary at p. Fixing the level K, we prove a bound (depending only on K) for the number of genuine cuspidal automorphic representations of Mp(4) ordinary at p and containing nonzero K-fixed vectors, as the holomorphic weight varies.
