No royal inscriptions of Erišum III have been found, but his name
appears in two king lists: the Assyrian
King List [/riao/KingLists/AssyrianKingList/index.html] (AKL) and the Synchronistic King List [/riao/KingLists/SynchronisticKingList/index.html] (SKL).
According to the former chronographic text, this Erišum held authority for thirteen years, was the son of Šū-Nīnua (or Kidin- Nīnua), and was the brother of his immediate predecessor (Šarma-Adad II). The SKL records that he was a contemporary of Gandaš, the first king of the Kassite dynasty, and Ea-gāmil, the last king of the Sealand I dynasty. Although scholars consider this synchronism to be false, it seems likely that Erišum ruled around the time of the fall of Babylon (1595 BC).
Yehonatan Hershkovitz
Yehonatan Hershkovitz, 'Erišum III', RIA 1: Inscriptions from the Origins of Assyria to Arik-dīn-ili, The RIA Project, 2024 [http://oracc.org/OldAssyrianPeriod/Belu-baniDynasty/ErishumIII/]