  The susceptibility amplitude ratio in the neighborhood of a uniaxial Lifshitz
point is calculated at one-loop level using field-theoretic and
$\epsilon_{L}$-expansion methods. We use the Schwinger parametrization of the
propagator in order to split the quadratic and quartic part of the momenta, as
well as a new special symmetry point suitable for renormalization purposes. For
a cubic lattice (d = 3), we find the result $\frac{C_{+}}{C_{-}} = 3.85$.
