On an exact mass formula of Shimura

DOI10.1215/S0012-7094-01-10716-3zbMath1023.11019OpenAlexW2006403544MaRDI QIDQ1847815

Jonathan P. Hanke, Jiu-Kang Yu, Gan, Wee Teck

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-10716-3

zbMATH Keywords

reductive groupmass formulaBruhat-Tits theoryHermitian spacemaximal latticeShimura's formula

Mathematics Subject Classification ID

Class numbers of quadratic and Hermitian forms (11E41) Classical groups (11E57) Linear algebraic groups over adèles and other rings and schemes (20G35)

Related Items (21)

A Simple Trace Formula for Algebraic Modular Forms ⋮ One-class genera of maximal integral quadratic forms ⋮ Unnamed Item ⋮ Mass formula of division algebras over global function fields ⋮ Finiteness theorems for congruence reflection groups. ⋮ On the superspecial loci of orthogonal type Shimura varieties ⋮ Automorphisms of extremal unimodular lattices in dimension 72 ⋮ Mass formulas and Eisenstein congruences in higher rank ⋮ Reflective obstructions of unitary modular varieties ⋮ Variations of mass formulas for definite division algebras ⋮ Quaternary quadratic lattices over number fields ⋮ On the computation of algebraic modular forms on compact inner forms of 𝐆𝐒𝐩₄ ⋮ An explicit growth condition for middle-degree cuspidal cohomology of arithmetically defined quaternionic hyperbolic \(n\)-manifolds ⋮ Genus 2 paramodular Eisenstein congruences ⋮ Incoherent Definite Spaces and Shimura Varieties ⋮ Explicit Calculations of Automorphic Forms for Definite Unitary Groups ⋮ Newton polygons arising from special families of cyclic covers of the projective line ⋮ Computing with Algebraic Automorphic Forms ⋮ Lattice Methods for Algebraic Modular Forms on Classical Groups ⋮ The mass of unimodular lattices ⋮ Group schemes and local densities.

Cites Work

• Volumes of S-arithmetic quotients of semi-simple groups. With an appendix by Moshe Jarden and Gopal Prasad
• Reductive groups on a local field. II. Groups schemes. Existence of valuated root datum
• Tamagawa numbers
• Unrefined minimal \(K\)-types for \(p\)-adic groups
• On the motive of a reductive group
• Jacquet functors and unrefined minimal \(K\)-types
• An exact mass formula for orthogonal groups.
• Construction of tame supercuspidal representations
• Schémas en groupes et immeubles des groupes classiques sur un corps local. II : groupes unitaires
• Haar Measure and the Artin Conductor
• Some exact formulas on quaternion unitary groups
• Unnamed Item
• Unnamed Item

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