  The Antarctic Impulsive Transient Antenna (ANITA), a NASA long-duration
balloon payload, searches for radio emission from interactions of
ultra-high-energy neutrinos in polar ice. The third flight of ANITA (ANITA-III)
was launched in December 2014 and completed a 22-day flight. We present the
results of three analyses searching for Askaryan radio emission of neutrino
origin. In the most sensitive of the analyses, we find one event in the signal
region on an expected a priori background of $0.7^{+0.5}_{-0.3}$. Though
consistent with the background estimate, the candidate event remains compatible
with a neutrino hypothesis even after additional post-unblinding scrutiny.
