Deconstructing the K -band number counts G. Barro 1 , J. Gallego 1 , P.G. P´ erez-Gonz´alez 1 , C. Eliche-Moral 1 , M.Balcells 2 , V.Villar 1 , N.Cardiel 1 , D. Cristobal-Hornillos 3 , A.Gil de Paz 1 , R. G´ uzman 4 ,R.Pell´o 5 , M. Prieto 2 and J.Zamorano 1 Abstract We present a study that links the NCs to the rest-frame luminosity functions (LFs) at the passbands probed by the observed K-band at different epochs. Making use of a large K-band selected sample in the Groth Field, HDFN and CDFS (∼0.27deg 2 ), we have derived highly reliable photometric redshift estimates that allow us to estimate LFs in the redshift range [0.25- 1.25]. We find that the larger flattening in the slope of the K-band NCs is mostly a consequence of a prominent decrease in the characteristic density (φ * ) around z∼1, and an almost flat evolution of M * . 1 Introduction The galaxy number counts (NCs) are one of the most simple and yet useful consistency test to be performed on galaxy surveys. In particular, NIR galaxy counts have been traditionally considered a centerpiece of distant galaxy stud- ies and a very useful method to constrain the models of galaxy evolution and cosmology. However, despite the apparent simplicity of the procedure, NCs represent sums of luminosity functions (LFs) modulated by shifts in appar- ent magnitude (due to the luminosity distance and the band redshift) and apparent number (due to to changes in the volume element and in the normal- ization of the LF). Thus, it is not surprising that, although the overall shape of the number counts is well defined, the full the interpretation in terms of the underlying galaxy populations still remains an open issue. Furthermore, there is a lack of agreement on the presence of some key features in the NCs such as a break in the slope of the K band number counts (K ∼17.5) [1, 2] or a roll over at very faint magnitudes. The origin of these controversies lies (1) Universidad Complutense de Madrid (UCM), e-mail: gbc@astrax.fis.ucm.es · (2) Instituto de Astrof´ ısica de Canarias (IAC) · (3) Instituto de Astrof´ ısica de Andaluc´ ıa (IAA) · (4) Universidad de Florida, USA · (5) Universit´ e de Toulouse, France 1