The K2 mission has recently begun to discover new and diverse planetary
systems. In December 2014 Campaign 1 data from the mission was released,
providing high-precision photometry for ~22000 objects over an 80 day timespan.
We searched these data with the aim of detecting further important new objects.
Our search through two separate pipelines led to the independent discovery of
K2-19b \& c, a two-planet system of Neptune sized objects (4.2 and 7.2
R⊕), orbiting a K dwarf extremely close to the 3:2 mean motion
resonance. The two planets each show transits, sometimes simultaneously due to
their proximity to resonance and alignment of conjunctions. We obtain further
ground based photometry of the larger planet with the NITES telescope,
demonstrating the presence of large transit timing variations (TTVs), and use
the observed TTVs to place mass constraints on the transiting objects under the
hypothesis that the objects are near but not in resonance. We then
statistically validate the planets through the \texttt{PASTIS} tool,
independently of the TTV analysis.Comment: 18 pages, 10 figures, accepted to A&A, updated to match published
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