  The possibility of detecting weak lensing effects from deep wide field
imaging surveys has open new means of probing the large-scale structures of the
Universe and measuring cosmological parameters. In this paper we present a
systematic study of the expected dependence of the low order moments of the
filtered gravitational local convergence with the power spectrum of the density
fluctuations and with the cosmological parameters Omega_0 and Lambda. The
results show a significant dependence with all these parameters. Though we note
that this degeneracy could be partially raised by considering two populations
of sources, at different redshifts, computing the third moment is more
promising since it is expected, in the quasi-linear regime and for Gaussian
initial conditions, to be only $\Omega_0$ dependent (with a slight degeneracy
with Lambda) when it is correctly expressed in terms of the second moment.
  More precisely we show that the variance of the convergence varies
approximately as P(k) Omega_0^{1.5} z_s^{1.5}, whereas the skewness varies as
Omega_0^{-0.8} z_s^{-1.35}, where P(k) is the projected power spectrum and z_s
the redshift of sources. Thus, used jointly they can provide both P(k) and
Omega_0. However, the dependence with the redshift of sources is large and
could be a major concern for a practical implementation.
  We have estimated the errors expected for these parameters in realistic
scenario and sketched what would be the observational requirements for doing
such measurements. A more detailed study of an observational strategy is left
for a second paper.
