LSJ
(on the accent v. Hdn. Gr. 1.491) Adv., on the very day, on the same day, immediately, A. Pers. 456, Ar. Ach. 522, al., Th. 2.12, D. 21.89; — also αὐθήμερα Hp. Fract. 24, Mochl. 42; Ion. αὐτημερόν Hdt. 2.122, 6.139 (but αὐθ- in Hp. Prog. 17, Aph. 4.10); Locr. αὐταμαρόν IG 9(1).334.33; Dor. αὐθαμέραν SIG 559.57 (Megalop.); Cret. αὐταμέριν GDI 4999 (Gortyn).
Liddell-Scott-Jones, Greek-English Lexicon (9th ed., 1940)