Fast Radio Burst FRB 20180916B in its host galaxy SDSS J015800.28+654253.0 at 149 Mpc is by far the closest-known FRB with a robust host galaxy association. The source also exhibits a 16.35day period in its bursting. Here we present optical and infrared imaging as well as integral field spectroscopy observations of FRB 20180916B with the WFC3 camera on the Hubble Space Telescope and the MEGARA spectrograph on the 10.4-m Gran Telescopio Canarias. The 60-90 milliarcsecond (mas) resolution of the Hubble imaging, along with the previous 2.3-mas localization of FRB 20180916B, allow us to probe its environment with a 30-60 pc resolution. We constrain any point-like star-formation or H II region at the location of FRB 20180916B to have an Hα luminosity L Hα 10 37 erg s −1 and, correspondingly, constrain the local star-formation rate to be 10 −4 M yr −1 . The constraint on

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High signal-to-noise ratio spectroscopic observations of the BL Lac object S4 0954+65 at the alleged redshift z = 0.367 are presented. This source was detected at gamma frequencies by MAGIC (TeV) and FERMI (GeV) telescopes during a remarkable outburst that occurred in February 2015, making the determination of its distance particularly relevant for our understanding of the properties of the Extragalactic Background Light. Contrary to previous reports on the redshift, we found that the optical spectrum is featureless at an equivalent width limit of ∼ 0.1 Å. A critical analysis of the existing observations indicates that the redshift is still unknown. Based on the new data we estimate a lower limit to the redshift at z ≥ 0.45.