Rajatarangini
Kalhana's Sanskrit chronicle of the kings of Kashmir in eight books, translated by M. A. Stein in 1900. For Amarnath: Book I, 267 (the Naga Susravas's lake like a sea of milk seen on the pilgrimage to Amareshvara, with Stein's note that the pilgrimage leads to the cave where Shiva is worshipped as an ice linga); Book II, 138 (Aryaraja worshipped lingas of snow above the forests in summer); Book VII, 183 to 185 (Suryamati's mathas, agraharas, tridents and banalingas at Amareshvara). Jonaraja's continuation records Sultan Zain-ul-Abidin's visit.
Sources: Kalhana's Rajatarangini, translated by M. A. Stein, vol. 1 (1900), archive.org dli.pahar.1527; M. M. Munshi, Tirtha of Amreshvara and Who discovered Amarnath? (ikashmir.net, a Kashmiri Pandit site); Dr Ramesh Kumar (R. K. Tamiri), Amaresvara Tradition in Kashmir Valley (ikashmir.net); Amarnath Temple, Wikipedia (the Amarnath Yatra page is the same article) · see Rajatarangini's web