ar X iv : m at h / 01 05 15 1 v 1 [ m at h . A C ] 1 7 M ay 2 00 1 The Hilbert Series of Pfaffian Rings ⋆

ar X iv : m at h / 05 01 13 9 v 2 [ m at h . FA ] 1 A ug 2 00 5 Stability of Adjointable Mappings in Hilbert C ∗ - Modules ∗

The generalized Hyers–Ulam–Rassias stability of adjointable mappings on Hilbert C∗-modules is investigated. As a corollary, we establish the stability of the equation f(x)∗y = xg(y)∗ in the context of C∗-algebras.

ar X iv : m at h / 01 05 23 2 v 1 [ m at h . N T ] 2 8 M ay 2 00 1 MODULAR CURVES OF GENUS 2

We prove that there are exactly 149 genus two curves C defined over Q such that there exists a nonconstant morphism π : X 1 (N) → C defined over Q and the jacobian of C is Q-isogenous to the abelian variety A f attached by Shimura to a newform f ∈ S 2 (Γ 1 (N)). We determine the corresponding newforms and present equations for all these curves.

ar X iv : m at h / 06 05 37 9 v 1 [ m at h . R A ] 1 5 M ay 2 00 6 AN EXTENDED FREUDENTHAL MAGIC SQUARE IN CHARACTERISTIC 3

Date: May 15, 2006. 2000 Mathematics Subject Classification. Primary 17B25.

ar X iv : m at h / 02 05 20 7 v 1 [ m at h . R T ] 1 9 M ay 2 00 2 Can p - adic integrals be computed ?

This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.

ar X iv : m at h / 06 05 35 5 v 1 [ m at h . G R ] 1 3 M ay 2 00 6 Axes in Outer Space