Inexistence, dimension formulas and classification for level one algebraic cusp forms

Gaëtan Chenevier & Olivier Taïbi (École Normale Supérieure)

28-Jan-2022, 13:30-15:00 (2 years ago)

Abstract: [Please note: there will be 2 talks, 45' each.]

In the first lecture we will explain how improvements on using an old tool in analytic number theory, Riemann-Weil's explicit formula for L-functions, allowed us to prove the non-existence of level one algebraic cusp forms for general linear groups over Q for lots of infinitesimal characters (=sets of Hodge weights). In the second lecture we will explain how these vanishing results yield an "effortless" method to compute the geometric side of Arthur's $L^2$-Lefschetz trace formula for split classical groups with the unit of the unramified Hecke algebra. We obtain dimension formulas as a consequence. Together these results give classification theorems for level one algebraic cusp forms in motivic weight <=23.

number theoryrepresentation theory

Audience: researchers in the topic

( slides | video )

Automorphic Project & Research Seminar

Series comments: For the rest of the 2022 spring semester, the seminar is switching to a new format, with the goal of preparing the audience for the IHES summer school on the Langlands program. We will have background talks only, with a talk on Monday evening or Tuesday morning ET, followed by a "watch party" on Tuesday morning or Tuesday evening ET, respectively, in order to accommodate participants from any time zone. The "watch parties" will feature a streaming of the recent talk, with the possibility to interrupt for questions, as in the live talks. (Recordings will be posted here after the watch party; click on "Past talks" on the seminar calendar to access them.)

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Organizers: Raphaël Beuzart-Plessis*, Tasho Kaletha*, Yiannis Sakellaridis*
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