Lewis & Short

2. ăvĕo (or, acc. to Quint. 1, 6, 21, hă-vĕo; cf. Spald. ad l. l. and Schneid. Gr. 1, p. 185), ēre, v. n. [v. 1. aveo init.], to be or fare well; except once in Mamert., used only in the imper. ave, aveto, avete, and inf. avere, as a form of salutation, both at meeting and separating, like salve and χαῖρε (hence, Fest. p. 13 explains it by gaudeo).

  1. I. In gen., Hail! God bless thee, farewell! adieu (prob. not used by Cic.): Caesar simulatque, Have, mihi dixit, statim exposuit, i. e. had saluted me, Cael. ap. Cic. Fam. 8, 16, 4: numquam dicis Ave, sed reddis etc., Mart. 3, 95, 1: Ave! gratiā plena, Dominus tecum! Vulg. Luc. 1, 28: Jesus occurrit illis dicens Avete! ib. Matt. 28, 9.
    In mock homage (eccl. Lat.): dixit Ave! Rabbi, Vulg. Matt. 26, 49; 27, 29; ib. Marc. 15, 18; ib. Joan. 19, 3.
    Haveto at the end of a letter, Cato ap. Sall. C. 35, 6; and Ave at the beginning, August. ap. Gell. 15, 7, 3: Marcus avere jubet, Mart. 3, 5, 10 al.
  2. II. Esp.
    1. A. As a morning greeting (diff. from vale, a greeting at separating in the evening; cf. Suet. Galb. 4: ut liberti servique mane salvere, vesperi valere sibi singuli dicerent): et matutinum portat ineptus ave, Mart. 1, 56, 6; 1, 56, 109 fin.; 4, 79, 4; 7, 39, 2.
    2. B. As a farewell to the dead, = vale: Atque in perpetuom, frater, ave atque vale, *Cat. 101, 10; and so frequently in inscriptions, Inscr. Orell. 2663; 4732; 4734; 4735; 4742. But in Martial avere is distinguished, as a greeting to the living, from valere, a greeting to the dead: Jam satis est, Afer: non vis avere: vale! Mart. 9, 7, 4. And thus the ambiguity of avere in the anecdote in Suet. Claud. 21 is to be explained: Emissurus (Claudius) Fucinum lacum naumachiam ante commisit. Sed cum proclamantibus naumachiariis, Ave (farewell), Imperator, morituri te salutant: respondisset, Avete vos (i. e. as dying), neque post hanc vocem, quasi venia data (since they interpreted the exclamation as live!), quisquam dimicare vellet, etc.
    3. C. As a mere expression of goodwill (eccl. Lat.): nec Ave ei dixeritis, nor bid him God-speed, Vulg. 2 Joan. 10, 11.
      Note: As finite verb: aveo plane Imperator et avebo … cum is avere jubeat, qui jam fecit, ut averem, Mamert. Grat. Act. ad Julian.