Principal value volumes of p-adic rational polyhedra

Wesley S. Cross

Vol. 233 (2007), No. 1, 71–89

DOI: 10.2140/pjm.2007.233.71

Abstract

This paper provides p-adic generalizations of some volume results from lattice convex geometry using the principal value integrals of Langlands and Shelstad. We prove a volume formula in the case of rational cones and conjecture that it extends to rational polyhedra.

Keywords

rational polyhedra, principal value integrals, p-adic numbers

Mathematical Subject Classification 2000

Primary: 52B20

Secondary: 11F85

Milestones

Received: 1 September 2006

Accepted: 18 April 2007

Published: 1 November 2007