The Infrastructure of a Global Field of Arbitrary Unit Rank

In this paper, we show a general way to interpret the infrastructure of a global field of arbitrary unit rank. This interpretation generalizes the prior concepts of the giant step operation and f-representations, and makes it possible to relate the infrastructure to the (Arakelov) divisor class group of the global field. In the case of global function fields, we present results that establish that effective implementation of the presented methods is indeed possible, and we show how Shanks' baby-step giant-step method can be generalized to this situation.Comment: Revised version. Accepted for publication in Math. Com

The global field of multi-family offices: An institutionalist perspective

We apply the notion of the organisational field to internationally operating multi-family offices. These organisations specialise on the preservation of enterprising and geographically dispersed families’ fortunes. They provide their services across generations and countries. Based on secondary data of Bloomberg’s Top 50 Family Offices, we show that they constitute a global organisational field that comprises two clusters of homogeneity. Clients may decide between two different configurations of activities, depending on their preferences regarding asset management, resource management, family management, and service architecture. The findings also reveal that multi-family offices make relatively similar value propositions all over the world. The distinctiveness of the clusters within the field is not driven by the embeddedness of the multi-family offices in different national environments or their various degrees of international experience. Rather, it is weakly affected by two out of four possible value propositions, namely the exclusiveness and the transparency of services

Interpolation of hypergeometric ratios in a global field of positive characteristic

In connection with each global field of positive characteristic we exhibit many examples of two-variable algebraic functions possessing properties consistent with a conjectural refinement of the Stark conjecture in the function field case recently proposed by the author (math.NT/0407535). Most notably, all examples are Coleman units. We obtain our results by studying rank one shtukas in which both zero and pole are generic, i.~e., shtukas not associated to any Drinfeld module.Comment: 25 pages, LaTe

Ergodicity of the action of K* on A_K

Connes gave a spectral interpretation of the critical zeros of zeta- and L-functions for a global field K using a space of square integrable functions on the space A_K/K* of adele classes. It is known that for K=Q the space A_K/K* cannot be understood classically, or in other words, the action of Q* on A_Q is ergodic. We prove that the same is true for any global field K, in both the number field and function field cases.Comment: 12 pages; minor change