The set of all divisors of , ordered according to increasing magnitude, is considered, and an upper bound on the gaps between consecutive ones is obtained. We are especially interested in the divisors nearest and obtain a lower bound on their distance.
We derive two identities for multiple basic hyper-geometric series associated with the unitary group. In order to get the two identities, we first present two known -exponential operator identities which were established in our earlier paper. From the two identities and combining them with the two -Chu-Vandermonde summations established by Milne, we arrive at our...