A q-analogue of de Rham cohomology

  • Kazuhiko Aomoto
  • Yoshifumi Kato


In this note we shall give a new formulation of Jackson integrals involved in basic hypergeometric functions through the classical Barnes representations. We define a q-analogue of de Rham cohomology which can be described by means of q-version of Sato’s b-functions and derive an associated holonomic q-difference system. The evaluation of its multiplicity will be given as the number of different asymptotic behaviours of Jackson integrals.


Toric Variety Newton Polyhedron Rational Polyhedral Cone Laurent Polynomial Ring Prehomogeneous Vector Space 
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Copyright information

© Springer-Verlag Tokyo 1991

Authors and Affiliations

  • Kazuhiko Aomoto
    • 1
  • Yoshifumi Kato
    • 2
  1. 1.Dept. of Mathematics, School of ScienceNagoya UniversityNagoyaJapan
  2. 2.Faculty of Science and TechnologyMeijo UniversityNagoya, 468Japan

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