The Arkansas, Birth Certificates, 1914-1917, database at www.ancestry.com has a certificate for Luther Edgar Davis, who was born on October 21, 1911, in Augusta, Woodruff County, Arkansas. His parents are listed as Robert Steve Davis and Gladys Matilda Heady.
https://www.ancestry.com/discoveryui-content/view/998979:61774?tid=&pid=&queryId=3255d32bb5a5c52b1d8886acca2129cc&_phsrc=daq1712&_phstart=successSource
The father has a familysearch.org profile:
https://www.familysearch.org/tree/person/details/LBJM-26T
So does the mother:
https://www.familysearch.org/tree/person/details/GMFC-RS1