Geometric zeta functions for higher rank $p$-adic groups
نویسندگان
چکیده
منابع مشابه
Computing Zeta Functions via p-Adic Cohomology
We survey some recent applications of p-adic cohomology to machine computation of zeta functions of algebraic varieties over finite fields of small characteristic, and suggest some new avenues for further exploration.
متن کاملSelberg zeta functions for spaces of higher rank
5 Introduction In 1956 A. Selberg introduced the zeta function Z(s) = c N ≥0 (1 − e −(s+N)l(c)), Re(s) >> 0, where the first product is taken over all primitive closed geodesics in a compact Riemannian surface of genus ≥ 2, equipped with the hyperbolic metric, and l(c) denotes the length of the geodesic c. Selberg proved that the product converges if the real part of s is large enough and that ...
متن کاملZETA FUNCTION OF REPRESENTATIONS OF COMPACT p-ADIC ANALYTIC GROUPS
Let G be a profinite group. We denote by rn(G) the number of isomorphism classes of irreducible n-dimensional complex continuous representations of G (so that the kernel is open in G). Following [20], we call rn(G) the representation growth function of G. If G is a finitely generated profinite group, then rn(G) < ∞ for every n if and only if G has the property FAb (that is, H/[H,H] is finite fo...
متن کاملZETA FUNCTIONS AND COUNTING FINITE p-GROUPS
We announce proofs of a number of theorems concerning finite p-groups and nilpotent groups. These include: (1) the number of p-groups of class c on d generators of order pn satisfies a linear recurrence relation in n; (2) for fixed n the number of p-groups of order pn as one varies p is given by counting points on certain varieties mod p; (3) an asymptotic formula for the number of finite nilpo...
متن کاملUniform p-adic cell decomposition and local zeta functions
The purpose of this paper is to give a cell decomposition for p-adic fields, uniform in p. This generalizes a cell decomposition for fixed p, proved by Denef [7], [9]. We also give some applications of our cell decomposition. A first implication is a uniform quantifier elimination for p-adic fields. Beiair [2], Delon [6] and Weispfenning [16] obtained quantifier elimination in other languages, ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 2014
ISSN: 0019-2082
DOI: 10.1215/ijm/1441790387