Lewis & Short

Jānŭārĭus, a, um, adj. [Janus], of or belonging to Janus.
Esp.,

  1. A. Januarius mensis, the month of January: auctio constituta in mensem Januarium, Cic. Agr. 1, 2, 4: Januario mense cura ut Romae sis, id. Att. 1, 2, 2.
    Also, subst.: Jānŭārĭus, i, m. (sc. mensis), January: a. d. VII. Idus Januarii, Caes. B. C. 1, 5; Hirt. B. G. 8, 2.
  2. B. Kalendae Januariae, the first day of January. This was a festival on which the Romans presented their good wishes to each other It was also regarded as a fortunate day on which to begin any undertaking, Cic. Agr. 1, 8, 26; 2, 3, 6; 2, 3, 8; Ov. F. 1, 64; Col. 11, 2: Nonae Januariae, Caes. B. C. 3, 6; Plin. 8, 45, 70, § 177.