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Number Theory Seminar
Seminar information archive ～01/13｜Next seminar｜Future seminars 01/14～
| Date, time & place | Wednesday 17:00 - 18:00 117Room #117 (Graduate School of Math. Sci. Bldg.) |
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| Organizer(s) | Naoki Imai, Shane Kelly |
Next seminar
2026/01/14
17:00-18:00 Room #117 (Graduate School of Math. Sci. Bldg.)
Takuro Fukayama (University of Tokyo)
The number of cuspidal representations over a function field and its behavior under base changes
Takuro Fukayama (University of Tokyo)
The number of cuspidal representations over a function field and its behavior under base changes
[ Abstract ]
Cuspidal representations of a reductive group are largely determined by their local components. In the function field case, it is important to describe how the number of cuspidal representations with given local conditions changes under base changes. Assuming Arthur's simple trace formula for function fields, this number should be given by the sum of Gross's L-functions attached to some reductive groups. In this talk, I will explain the expression of the sum of L-functions and its behavior under base changes for some classical groups.
Cuspidal representations of a reductive group are largely determined by their local components. In the function field case, it is important to describe how the number of cuspidal representations with given local conditions changes under base changes. Assuming Arthur's simple trace formula for function fields, this number should be given by the sum of Gross's L-functions attached to some reductive groups. In this talk, I will explain the expression of the sum of L-functions and its behavior under base changes for some classical groups.
