Most Lensed Quasars at $z>6$ are Missed by Current Surveys
  The discovery of the first strongly lensed $(\mu \approx 50)$ quasar at $z>6$
(J0439+1634) represents a breakthrough in our understanding of the early
Universe. We derive the theoretical consequences of the new discovery. We
predict that the observed population of $z > 6$ quasars should contain many
sources with magnifications $\mu \lesssim 10$ and with image separations below
the resolution threshold. Additionally, current selection criteria could have
missed a substantial population of lensed $z > 6$ quasars, due to the
contamination of the drop-out photometric bands by lens galaxies. We argue that
this predicted population of lensed $z>6$ quasars would be misclassified and
mixed up with low-$z$ galaxies. We quantify the fraction of undetected quasars
as a function of the slope of the bright end of the quasar luminosity function,
$\beta$. For $\beta \lesssim 3.6$, we predict that the undetected lensed
quasars could reach half of the population, whereas for $\beta \gtrsim 4.5$ the
vast majority of the $z > 6$ quasar population is lensed and still undetected.
This would significantly affect the $z > 6$ quasar luminosity function and
inferred black hole mass distributions, with profound implications for the
ultraviolet, X-ray, and infrared cosmic backgrounds and the growth of early
quasars.
