pairs, then the characteristic scale is found through the three-dimensional (3D) two-point correlation function. Here instead, we use the two-dimensional (2D) version of this correlation function, that is, the two-point angular correlation function (2PACF), using quasars located in a thin redshift shell. This analysis is only possible now because the current dataset is spatially dense enough to allow for the measurement of the angular BAO signal with high statistical significance.

The two-point angular correlation function
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One way to characterize the clustering of galaxies, quasars, and other cosmological tracers is through the two-point correlation function (2PCF) . The 2PCF is based on counting pairs of cosmic objects in a data set (quasars, for example) $DD(s)$ at a given comoving 3D distance $s$ and compare this with the number of pairs $RR(s)$ from a random set.

The most used 2PCF estimator in astrophysical applications is the Landy-Szalay (LS) [@Landy-Szalay], because it returns the smallest deviations for a given cumulative probability, besides to have no bias and minimal variance [@Kerscher]. This estimator is defined by $$\begin{aligned}
\label{2PCF}
    \xi(s) \equiv \frac{DD(s) - 2DR(s) + RR(s)}{RR(s)},
    \end{aligned}$$ where $DR(s)$ counts the pairs, one in the data set and the other in the random set, 