Skip to main content
SpringerLink
Log in

Arrangements with one bounded component andp-adic integrals

  • Published:
manuscripta mathematica Aims and scope Submit manuscript

Abstract

In this article we study arrangementsA, such that ℝn\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 ap-adic integral to each such arrangement and proof that this integral can be written as a product ofp-adic beta functions. This is analogous to results of Varchenko and Loeser for integrals over ℝ and character sums over finite fields respectively.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Barnabei, A. Brini, G.-C. Rota, Theory of Mobius functions, Uspehi Mat. Nauk 41 (1986), 135–187

    MATH  MathSciNet  Google Scholar 

  2. J. Denef, Report on Igusa’s local zeta function, Astérisque 201–202–203 (1991), 359–386

    MathSciNet  Google Scholar 

  3. J.I. Igusa, Lectures on forms of higher degree, Tata Institute of Fundamental Research, Bombay, 1978

    MATH  Google Scholar 

  4. F. Loeser, Arrangements d’hyperplans et sommes de Gauss, Ann. scient. Ec. Norm. Sup., 4e série 24 (1991), 379–400

    MATH  MathSciNet  Google Scholar 

  5. P. Orlik—H. Terao, Arrangements of hyperplanes, Springer Verlag, Berlin Heidelberg 1992

    MATH  Google Scholar 

  6. P.J. Sally, Jr. and M.H. Toublesson, Special functions on locally compact fields, Washington University, St. Louis, Mo, USA, 279–309

  7. A.N. Varchenko, The Euler beta-function, the Vandermonde determinant, Legendre’s equation and critical values of linear functions on a configuration of hyperplanes I, Math. USSR Izvestiya, Vol. 35 (1990), 543–571

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Leuven, Celestijnenlaan 200B, 3001, Leuven, Belgium

    Philippe Jacobs & Ann Laeremans

Authors
  1. Philippe Jacobs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ann Laeremans
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jacobs, P., Laeremans, A. Arrangements with one bounded component andp-adic integrals. Manuscripta Math 85, 33–44 (1994). https://doi.org/10.1007/BF02568182

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02568182

Keywords

Search

Navigation