ARRANGEMENTS WITH ONE BOUNDED COMPONENT AND P-ADIC INTEGRALS

In this article we study arrangements A, such that R(n)/A has exactly one bounded component. We obtain a result about their structure which gives us a method to construct all combinatorially different such arrangements in a given dimension. (A complete list for dimensions 1,2,3 and 4 is included). Furthermore we associate a p-adic integral to each such arrangement and proof that this integral can be written as a product of p-adic beta functions. This is analogous to results of Varchenko and Loeser for integrals over R and character sums over finite fields respectively.