相关论文: Representation zeta functions of some nilpotent gr…

Inspired by work surrounding Igusa's local zeta function, we introduce topological representation zeta functions of unipotent algebraic groups over number fields. These group-theoretic invariants capture common features of established…

This is the second of two papers introducing and investigating two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. In the first part, we proved some of their properties such as…

Let $\mathbf{G}$ be a unipotent group scheme defined in terms of a nilpotent Lie lattice over the ring $\mathcal{O}$ of integers of a number field. We consider bivariate zeta functions of groups of the form $\mathbf{G}(\mathcal{O})$…

We study representation zeta functions of finitely generated, torsion-free nilpotent groups which are rational points of unipotent group schemes over rings of integers of number fields. Using the Kirillov orbit method and p-adic…

We introduce and study multivariate zeta functions enumerating subrepresentations of integral quiver representations. For nilpotent such representations defined over number fields, we exhibit a homogeneity condition that we prove to be…

We develop techniques for computing zeta functions associated with nilpotent groups, not necessarily associative algebras, and modules, as well as Igusa-type zeta functions. At the heart of our method lies an explicit convex-geometric…

We compute the representation and class counting zeta functions for a family of torsion-free finitely generated nilpotent groups of nilpotency class $2$. These groups arise from a generalisation of one the families of unipotent groups…

We give a sufficient criterion for generic local functional equations for submodule zeta functions associated to nilpotent algebras of endomorphisms defined over number fields. This allows us, in particular, to prove various conjectures on…

We consider pro-isomorphic zeta functions of the groups $\Gamma(\mathcal{O}_K)$, where $\Gamma$ is a unipotent group scheme defined over $\mathbb{Z}$ and $K$ varies over all number fields. Under certain conditions, we show that these…

We introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups. They allow us to establish that the representation zeta functions of…

This is the first of two papers in which we introduce and study two bivariate zeta functions associated to unipotent group schemes over rings of integers of number fields. One of these zeta functions encodes the numbers of isomorphism…

We study zeta functions enumerating finite-dimensional irreducible complex linear representations of compact p-adic analytic and of arithmetic groups. Using methods from p-adic integration, we show that the zeta functions associated to…

We compute the local pro-isomorphic zeta functions at all but finitely many primes for a certain family of class-two-nilpotent Lie lattices of even rank, parametrized by irreducible non-linear polynomials $f(x) \in \mathbb{Z} [x]$, that…

We study zeta functions enumerating subalgebras or ideals of Lie algebras over finite field of prime order $\mathbb{F}_p$. We first develop a general blueprint method for computing zeta functions of $\mathbb{F}_p$-Lie algebras, and…

We give a short introduction to the subject of representation growth and representation zeta functions of groups, omitting all proofs. Our focus is on results which are relevant to the study of arithmetic groups in semisimple algebraic…

We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free $d$-generator Lie rings $\mathfrak{f}_{c,d}$ of nilpotency class $c$ for all $c\leq2$ and for $(c,d)\in\{(3,3),(3,2),(4,2)\}$. We apply…

We develop a practical method for computing local zeta functions of groups, algebras, and modules in fortunate cases. Using our method, we obtain a complete classification of generic local representation zeta functions associated with…

We compute explicitly Dirichlet generating functions enumerating finite-dimensional irreducible complex representations of various $p$-adic analytic and adelic profinite groups of type $\mathsf{A}_2$. This has consequences for the…

In this paper, we explore the properties of zeta functions associated with infinite graphs of groups that arise as quotients of cuspidal tree-lattices, including all non-uniform arithmetic quotients of the tree of rank one Lie groups over…

Using the Kirillov orbit method, novel methods from p-adic integration and Clifford theory, we study representation zeta functions associated to compact p-adic analytic groups. In particular, we give general estimates for the abscissae of…