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We study the space density evolution of active galactic nuclei (AGN) usingthe $610 \ \mathrm{MHz}$ radio survey of the XXL-North field, performed withthe Giant Metrewave Radio Telescope (GMRT). The survey covers an area of $30.4\ \mathrm{deg}^2$, with a beamsize of $6.5 \ \mathrm{arcsec}$. The survey isdivided into two parts, one covering an area of $11.9 \ \mathrm{deg}^2$ with $1\sigma$ rms noise of $200\ \mathrm{\mu Jy \ beam^{-1}}$ and the other spanning$18.5 \ \mathrm{deg}^2$ with rms noise of $45\ \mathrm{\mu Jy \ beam^{-1}}$. Weextracted the catalog of radio components above $7 \sigma$. The catalog wascross-matched with a multi-wavelength catalog of the XXL-North field (coveringabout $80 \%$ of the radio XXL-North field) using a likelihood ratio method,which determines the counterparts based on their positions and their opticalproperties. The multi-component sources were matched visually with the aid of acomputer code: Multi-Catalog Visual Cross-Matching (MCVCM). A flux density cutabove $1\ \mathrm{mJy}$ selects AGN hosts with a high purity in terms of starformation contamination based on the available source counts. Aftercross-matching and elimination of observational biases arising from surveyincompletenesses, the number of remaining sources was $1150$. We constructedthe rest-frame $1.4 \ \mathrm{GHz}$ radio luminosity functions of these sourcesusing the maximum volume method. This survey allows us to probe luminosities of$ 23 \lesssim \log(L_{1.4 \ \mathrm{GHz}}[\mathrm{W/Hz}]) \lesssim 28$ up toredshifts of $z \approx 2.1$. Our results are consistent with the results fromthe literature in which AGN are comprised of two differently evolvingpopulations, where the high luminosity end of the luminosity functions evolvesmore strongly than the low-luminosity end.

The XXL Survey. XLI. Radio AGN luminosity functions based on the GMRT $610 \ \mathrm{MHz}$ continuum observations