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We measure the imprint of primordial baryon acoustic oscillations (BAO) inthe correlation function of Ly$\alpha$ absorption in quasar spectra from theBaryon Oscillation Spectroscopic Survey (BOSS) and the extended BOSS (eBOSS) inData Release 14 (DR14) of the Sloan Digital Sky Survey (SDSS)-IV. In additionto 179,965 spectra with absorption in the Lyman-$\alpha$ (Ly$\alpha$) region,we use, for the first time, Ly$\alpha$ absorption in the Lyman-$\beta$ regionof 56,154 spectra. We measure the Hubble distance, $D_H$, and the comovingangular diameter distance, $D_M$, relative to the sound horizon at the dragepoch $r_d$ at an effective redshift $z=2.34$. Using a physical model of thecorrelation function outside the BAO peak, we find $D_H(2.34)/r_d=8.86\pm 0.29$and $D_M(2.34)/r_d=37.41\pm 1.86$, within 1$\sigma$ from the flat-$\Lambda$CDMmodel consistent with CMB anisotropy measurements. With the addition ofpolynomial "broadband" terms, the results remain within one standard deviationof the CMB-inspired model. Combined with the quasar-Ly$\alpha$cross-correlation measurement presented in a companion paper Blomqvist19, theBAO measurements at $z=2.35$ are within 1.7$\sigma$ of the predictions of thismodel.

Baryon acoustic oscillations at z = 2.34 from the correlations of Ly$\alpha$ absorption in eBOSS DR14