  We derive generalizations of the Cherednik-Macdonald constant term identities
associated to root systems which depend, besides on the usual multiplicity
function, symmetrically on two quasi-periods. They are natural analogues of the
Cherednik-Macdonald constant term q-identities in which the deformation
parameter q is allowed to have modulus one. They unite the Cherednik-Macdonald
constant term q-identities with closely related Jackson p-integral identities
due to Macdonald, where the deformation parameter p is related to q by modular
inversion.
