We present measurements of the local primordial non-Gaussianity parameter fNLloc from the clustering of 343,708 quasars with redshifts 0.8 < z < 2.2 distributed over 4808 square degrees from the final data release (DR16) of the extended Baryon acoustic Oscillation Spectroscopic Survey (eBOSS), the largest volume spectroscopic survey up to date. Our analysis is performed in Fourier space, using the power spectrum monopole at very large scales to constrain the scale dependent halo bias. We carefully assess the impact of systematics on our measurement and test multiple contamination removal methods. We demonstrate the robustness of our analysis pipeline with EZ-mock catalogues that simulate the eBOSS DR16 target selection. We find $f_mathrm{NL}=-12pm 21$ (68% confidence) for the main clustering sample including quasars with redshifts between 0.8 and 2.2, after exploiting a novel neural network scheme for cleaning the DR16 sample and in particular after applying redshift weighting techniques, designed for non-Gaussianity measurement from large scales structure, to optimize our analysis, which improve our results by 37%.
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