Aims. The main goal of this work is to measure rotation periods of the M-type dwarf stars being observed by the CARMENES exoplanet survey to help distinguish radial-velocity signals produced by magnetic activity from those produced by exoplanets. Rotation periods are also fundamental for a detailed study of the relation between activity and rotation in late-type stars. Methods. We look for significant periodic signals in 622 photometric time series of 337 bright, nearby M dwarfs obtained by long-time baseline, automated surveys (MEarth, ASAS, SuperWASP, NSVS, Catalina, ASAS-SN, K2, and HATNet) and for 20 stars which we obtained with four 0.2–0.8 m telescopes at high geographical latitudes. Results. We present 142 rotation periods (73 new) from 0.12 d to 133 d and ten long-term activity cycles (six new) from 3.0 a to 11.5 a. We compare our determinations with those in the existing literature; we investigate the distribution of Prot in the CARMENES input catalogue, the amplitude of photometric variability, and their relation to v sini and pEW(Hα); and we identify three very active stars with new rotation periods between 0.34 d and 23.6 d.

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Magnification bias is a gravitational lensing effect that is normally overlooked because it is considered sub-optimal in comparison with the lensing shear. Thanks to the demonstrated optimal characteristics of the sub-millimetre galaxies (SMGs) for lensing analysis, in this work we were able to measure the magnification bias produced by a sample of QSOs acting as lenses, 0.2 13.6−0.4+0.9, also confirmed by the mass density profile analysis (M200c∼ 1014 M⊙). These mass values indicate that we are observing the lensing effect of a cluster size halo signposted by the QSOs, as in previous studies of the magnification bias. Moreover, we were able to estimate the lensing convergence, κ(θ), for our magnification bias measurements down to a few kpcs. The derived mass density profile is in good agreement with a Navarro-Frank-White (NFW) profile. We also attempt an estimation of the halo mass and the concentration parameters, obtaining MNFW=1.0+0.4−0.2×1014 M⊙ and C=3.5−0.3+0.5. This concentration value is rather low and it would indicate that the cluster halos around these QSOs are unrelaxed. However, higher concentration values still provides a compatible fit to the data.