Macedo Lins de Araujo, Paula: Bivariate representation and conjugacy class zeta functions associated to unipotent group schemes. 2019
Inhalt
- Introduction and summary of main results
- Zeta functions related to representations and conjugacy classes of groups
- Main results
- Organisation of chapters
- Preliminaries
- Group schemes obtained from nilpotent Lie lattices
- Some p-adic integrals
- Principalisation of ideals
- Two complex variables
- Double series
- Convergence of bivariate Euler products
- Arithmetic properties of ZG(O)
- Euler decomposition
- Bivariate zeta functions in terms of p-adic integrals
- Twist representation zeta functions
- Local functional equations—proof of Theorem 1
- Analytic properties of ZG(O)
- Groups of type F, G, and H
- Bivariate conjugacy class zeta functions—Proof of Theorem 2
- Commutator matrices
- Conjugacy class zeta functions of groups of type F
- Conjugacy class zeta functions of groups of type G
- Conjugacy class zeta functions of groups of type H
- Bivariate representation zeta functions—proof of Theorem 3
- Hyperoctahedral groups and functional equations
- Index
- List of symbols
- References