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The importance of studying the Gaia DR2 parallax zero-point by external meanswas underlined by Lindegren et al. (2018), and initiated by several worksmaking use of Cepheids, eclipsing binaries, and asteroseismology. Despite avery efficient elimination of basic-angle variations, a small fluctuationremains and shows up as a small offset in the Gaia DR2 parallaxes. By combiningastrometric, asteroseismic, spectroscopic, and photometric constraints, weundertake a new analysis of the Gaia parallax offset for nearly 3000 red-giantbranch (RGB) and 2200 red clump (RC) stars observed by Kepler, as well as about500 and 700 red giants (both RGB and RC) selected by the K2 GalacticArchaeology Program in campaigns 3 and 6. Engaging into a thorough comparisonof the astrometric and asteroseismic parallaxes, we are able to highlight theinfluence of the asteroseismic method, and measure parallax offsets in theKepler field that are compatible with independent estimates from literature andopen clusters. Moreover, adding the K2 fields to our investigation allows us toretrieve a clear illustration of the positional dependence of the zero-point,in general agreement with the information provided by quasars. Lastly, weinitiate a two-step methodology to make progress in the simultaneouscalibration of the asteroseismic scaling relations and of the Gaia DR2 parallaxoffset, which will greatly benefit from the gain in precision with the thirdData Release of Gaia.

New light on the Gaia DR2 parallax zero-point: influence of the asteroseismic approach, in and beyond the Kepler field