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Although we have evidence of epics, there are no names of authors from the period which can be connected to them. There are not even any works in their original forms.
According to Mary Boyce, in Parthian Writing and Literature (from Cambridge History of Iran, Volume 3(2)),
No Parthian literature survives from the Parthian period in its original form. The only works of any length which exist in the Parthian language were composed under Sasanian rule. For the literature of older times we are dependent on Middle Persian redactions, or even on Persian and Georgian versions of these, to give at second or third remove some impression of the nature and scope of what has been lost.
As to the reasons for Parthian literature not surviving,
One reason for the scale of the loss is presumably that Parthian literature, both religious and secular, was oral, composed and transmitted without the use of books.
Secular oral literature was 'cultivated' memorized and transmitted by a gosan (a kind of minstrel) and
appears to have been almost wholly in verse, sung, and accompanied by a musical instrument.
Elements of Parthian literature have been preserved in some later writings, such as the apocryphal Acts of St Thomas in which can
be found the beautiful “Hymn of the Pearl” or “Hymn of the Soul" This Syriac poem not only contains Parthian loan-words, but uses symbolism drawn from the circumstances of the Parthian empire, which in it represents the Kingdom of Heaven.
Additionally, we have later versions of "the romance of Vis o Rāmin" and Draxt ī asūrīg...or “The Babylonian Tree,” There is also
a fragment of the Kayanian epic cycle [which] survives in the Ayādgār ī Zarērān...or “Memorial of Zarēr.” This heroic poem, transmitted in a late post-Sasanian Middle Persian redaction (perhaps of the 9th century), is undoubtedly of Parthian origin, as can be seen from the use of Parthian words and expressions. It relates the exploits of the Iranian hero Zarēr in the confrontation of the Iranians under King Wištāsp with King Arǰāsp and his Xiyonians.
Even Parthian inscriptions
are few and short since the use of Aramaic and Greek was still frequent at that time; all longer Parthian inscriptions actually date from the early Sasanian period, when the first kings of the new dynasty chose to incorporate a Parthian version in their trilingual or bilingual inscriptions.
The surviving inscriptions and parchments contain details of, for example, sales of property inventory lists and the first lines of a business letter rather than literature.
For histories, we are heavily dependent on Roman writers but there are some sources from elsewhere, including the Chinese diplomat Zhang Qian and the Armenian historian Movses Khorenatsi, though the reliability of the latter (on Parthia) is in some doubt.