  We investigate the evolution on secular time-scales of a radially extended
debris disc under the influence of a system of two coplanar planets interior to
the disc, showing that the secular resonances of the system can produce a
depleted region in the disc by exciting the eccentricities of planetesimals.
Using Laplace-Lagrange theory, we consider how the two exterior secular
resonance locations, time-scales and widths depend on the masses, semi-major
axes and eccentricities of the planets. In particular, we find that unless the
resonances are very close to each other, one of them is very narrow and
therefore unimportant for determining the observable structure of the disc. We
apply these considerations to the debris disc of HD 107146, identifying
combinations of the parameters of a possible unobserved two-planet system that
could configure the secular resonances appropriately to reproduce the depletion
observed in the disc. By performing N-body simulations of such systems, we find
that planetesimal eccentricities do indeed become large near the theoretical
secular resonance locations. The N-body output is post-processed to set the
initial surface density profile of the disc, and to include the possible
effects of collisional depletion. We find that it is possible to obtain a
double-ringed disc in these simulations but not an axisymmetric one, with the
inner ring having an offset whose magnitude depends on the eccentricities of
the planets, and the outer ring showing spiral structure.
