  We report on Doppler observations of three transiting planet candidates that
were detected during Campaign 1 of the K2 mission. The Doppler observations
were conducted with FIES, HARPS-N and HARPS. We measure the mass of K2-27b
(EPIC 201546283b), and provide constraints and upper limits for EPIC 201295312b
and EPIC 201577035b. K2-27b is a warm Neptune orbiting its host star in 6.77
days and has a radius of $4.45^{+0.33}_{-0.33}~\mathrm{R_\oplus}$ and a mass of
$29.1^{+7.5}_{-7.4}~\mathrm{M_\oplus}$, which leads to a mean density of
$1.80^{+0.70}_{-0.55}~\mathrm{g~cm^{-3}}$. EPIC 201295312b is smaller than
Neptune with an orbital period of 5.66 days, radius
$2.75^{+0.24}_{-0.22}~\mathrm{R_\oplus}$ and we constrain the mass to be below
$12~\mathrm{M_\oplus}$ at 95% confidence. We also find a long-term trend
indicative of another body in the system. EPIC 201577035b, previously confirmed
as the planet K2-10b, is smaller than Neptune orbiting its host star in 19.3
days, with radius $3.84^{+0.35}_{-0.34}~\mathrm{R_\oplus}$. We determine its
mass to be $27^{+17}_{-16}~\mathrm{M_\oplus}$, with a 95% confidence uppler
limit at $57~\mathrm{M_\oplus}$, and mean density $2.6^{+2.1}_{-1.6}~{\rm
g~cm}^{-3}$. These measurements join the relatively small collection of planets
smaller than Neptune with measurements or constraints of the mean density. Our
code for performing K2 photometry and detecting planetary transits is now
publicly available.
