Related papers: Towards a dichotomy for the Reidemeister zeta func…

We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational…

We study the motivic Grothendieck group of algebraic varieties from the point of view of stable birational geometry. In particular, we obtain a counter-example to a conjecture of M. Kapranov on the rationality of motivic zeta-function.

In this paper we study the longstanding conjecture of whether there exists a noninner automorphism of order $p$ for a finite non-abelian $p$-group. We prove that if $G$ is a finite non-abelian $p$-group such that $G/Z(G)$ is powerful then…

We explore the structure of the p-adic automorphism group Gamma of the infinite rooted regular tree. We determine the asymptotic order of a typical element, answering an old question of Turan. We initiate the study of a general dimension…

We examine "partition zeta functions" analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties -- those…

We determine the structure of automorphism groups of finite graphs of bounded Hadwiger number. Our proof includes a structural analysis of finite edge-transitive graphs. In particular, we show that for connected, $K_{h+1}$-minor-free,…

We show an equality between the analytic torsion and the absolute value at the zero point of the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an acyclic flat vector bundle obtained by the…

The aim of this note is to give simple proofs of some results of Reichstein and Youssin (math.AG/9903162) about the behaviour of fixed points of finite group actions under rational maps. Our proofs work in any characteristic. We also give a…

For a non-compact hyperbolic 3-manifold with cusps we prove an explicit formula that relates the regularized analytic torsion associated to the even symmetric powers of the standard representation of SL_2(C) to the corresponding…

In \cite{BAMU}, an ergodic theorem \`a la Birkhoff-von Neumann for the action of the fundamental group of a compact negatively curved manifold on the boundary of its universal cover is proved. A quick corollary is the irreducibility of the…

We give a dynamical description, in terms of a Weil-type zeta function, to the holomorphic torsion with coefficients for certain compact Hermitian locally symmetric manifolds, whose connected group G of isometries of the universal cover has…

Let $F_{2,d}$ denote the free class-2-nilpotent group on $d$ generators. We compute the normal zeta functions $\zeta^\triangleleft_{F_{2,d}}(s)$, prove that they satisfy local functional equations and determine their abscissae of…

We initiate the study of spectral zeta functions $\zeta_{X}$ for finite and infinite graphs $X$, instead of the Ihara zeta function, with a perspective towards zeta functions from number theory and connections to hypergeometric functions.…

Let G be a torsion--free abelian group of finite rank. The automorphism group Aut(G) acts on the set of maximal independent subsets of G. The orbits of this action are the isomorphism classes of indecomposable decompositions of G. G…

Let $K$ be a complete non-archimedean field of characteristic $0$ equipped with a discrete valuation. We establish the rationality of the Artin-Mazur zeta function on the Julia set for any subhyperbolic rational map defined over $K$ with a…

Take $(R, \mathfrak{m})$ any normal Noetherian domain, either local or $\mathbb{N}$-graded over a field. We study the question of when $R$ satisfies the uniform symbolic topology property (USTP) of Huneke, Katz, and Validashti: namely, that…

The zeta-function of a complex variety is a power series whose nth coefficient is the nth symmetric power of the variety, viewed as an element in the Grothendieck ring of complex varieties. We prove that the zeta-function of a surface is…

Given a torsion-free $p$-adic analytic pro-$p$ group $G$ with $\mathrm{dim}(G) < p$, we show that the self-similar actions of $G$ on regular rooted trees can be studied through the virtual endomorphisms of the associated $\mathbb{Z}_p$-Lie…

We introduce a new method to calculate local normal zeta functions of finitely generated, torsion-free nilpotent groups. It is based on an enumeration of vertices in the Bruhat-Tits building for Sl_n(Q_p). It enables us to give explicit…

We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts,…