Anthony Barber and Sree Padma note that "historians of Buddhist thought have been aware for quite some time that such pivotally important Mahayana Buddhist thinkers as Nāgārjuna, Dignaga, Candrakīrti, Āryadeva, and Bhavaviveka, among many others, formulated their theories while living in Buddhist communities in Āndhra." They note that the ancient Buddhist sites in the lower Kṛṣṇa Valley, including Amaravati, Nāgārjunakoṇḍā and Jaggayyapeṭa "can be traced to at least the third century BCE, if not earlier." Akira Hirakawa notes the "evidence suggests that many Early Mahayana scriptures originated in South India."
The ancient buddhist site  in the lower Krsna Valley can be traced to at least what century BCE?
third