  We investigate the connection between the local electron correlation and the
momentum dependence of the spin susceptibility and the superconducting gap
functions in Sr$_2$RuO$_4$, using density-functional theory combined with
dynamical mean-field theory. Adopting frequency-dependent twoparticle vertex
moves the zero energy spin susceptibility peaks towards the Brillouin zone
center, compared with random-phase approximation which basically retains the
peak positions closer to the Brillouin zone boundary as determined by the
Fermi-surface nesting. We find that dxy orbital plays a central role here via
its enhanced correlation strength. Solving the linearized Eliashberg equation
from this spin susceptibility, prime candidates of the superconducting gap
symmetry are a s-wave, along with a nearly degenerate d-wave solution, all in
spin singlet. Furthermore, another set of degenerate spin singlet gap functions
emerges, odd with respect to k-point as well as orbital exchanges. We show that
the stability of these gap functions are strongly dependent on the peak
position of the spin susceptibility in the Brillouin zone.

Strongly Correlated Electrons;Superconductivity