A q-analogue of de Rham cohomology
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.
KeywordsToric Variety Newton Polyhedron Rational Polyhedral Cone Laurent Polynomial Ring Prehomogeneous Vector Space
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