  A large-N diagrammatic approach is used to study coupled quantum dots in a
parallel geometry. We show that the Friedel sum rule (FSR) holds at lowest
order in a 1/N expansion for this system, thereby suggesting that the ground
state is a Fermi liquid. Using the FSR together with the dot occupancy, we
compute the dot system's conductance. Our finding that the 1/N expansion
indicates the system is a Fermi liquid is in agreement with both prior results
based on the Bethe ansatz and slave boson mean field theory.
