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We report on Doppler observations of three transiting planet candidates thatwere detected during Campaign 1 of the K2 mission. The Doppler observationswere conducted with FIES, HARPS-N and HARPS. We measure the mass of K2-27b(EPIC 201546283b), and provide constraints and upper limits for EPIC 201295312band EPIC 201577035b. K2-27b is a warm Neptune orbiting its host star in 6.77days 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 thanNeptune 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 trendindicative of another body in the system. EPIC 201577035b, previously confirmedas the planet K2-10b, is smaller than Neptune orbiting its host star in 19.3days, with radius $3.84^{+0.35}_{-0.34}~\mathrm{R_\oplus}$. We determine itsmass to be $27^{+17}_{-16}~\mathrm{M_\oplus}$, with a 95% confidence upplerlimit at $57~\mathrm{M_\oplus}$, and mean density $2.6^{+2.1}_{-1.6}~{\rmg~cm}^{-3}$. These measurements join the relatively small collection of planetssmaller than Neptune with measurements or constraints of the mean density. Ourcode for performing K2 photometry and detecting planetary transits is nowpublicly available.

The K2-ESPRINT Project II: Spectroscopic follow-up of three exoplanet systems from Campaign 1 of K2