The effects of lensing by local structures on the dipole of radio source
  counts
  Our peculiar motion in a homogeneous and isotropic universe imprints a dipole
in the cosmic microwave background (CMB) temperature field and similarly
imprints a dipole in the distribution of extragalactic radio sources on the
sky. Each of these effects have been measured, however each of these
measurements give different results for the velocity of our motion through the
Universe: the radio dipole measurements finds the speed of our motion to be
around three times larger than that of the CMB. Here we show the effects of the
previously unconstrained lensing dipole, whereby necessarily local structures
(required for large angular lensing scales) will distort the distribution of
radio sources on the sky. We find that the inclusion of these effects does not
reduce the tension between the CMB and radio source dipole measurements however
without their inclusion future extragalactic number counts could lead to
incorrect inferences of our peculiar motion. In addition we can constrain the
size of the lensing dipole to be $\kappa < 3 \cdot 10^{-2}$ at the $2 \sigma$
level.
