Galactic open cluster Cepheids -- a census based on Gaia EDR3.

In the Gaia era, the membership analysis and parameter determination of open clusters (OCs) are more accurate. We performed a census of OC's classical Cepheids based on Gaia Early Data Release 3 (EDR3) and obtained a sample of 33 OC Cepheids fulfilling the constraints of the spatial position, proper motion, parallax and evolution state. 13 of 33 OC Cepheids are newly discovered. Among them, CM Sct is the first first-crossing Cepheids with direct evidence of evolution. DP Vel is likely a fourth- or fifth-crossing Cepheids. Based on independent distances from OCs, W_1-band period-luminosity relation of Cepheids is determined with a 3.5% accuracy: = -(3.274 +- 0.090) log P - (-2.567 +- 0.080). The Gaia-band period-Wesenheit relation agrees well with Ripepi et al. (2019). A direct period-age relation for fundamental Cepheids are also determined based on OC's age, that is log t = -(0.638 +- 0.063) log P + (8.569 +- 0.057).