Source: TW
The saiddhAntika scripture kAlottara (in a somewhat corrupt part of the currently available text) specifies a mantra called amR^itarudra in a list of Vedic mantra-s to be recited during the rudrAbhiSheka performed with a bovine horn. However, it is not entirely clear what mantra is meant by this name.
One likely candidate is the tryambaka R^ik. However, there is another archaic connection that should be mentions in this regard (especially given that the kAlottara mentioned the amR^itarudra in the context of atharvan mantra-s). Chapter 3 of the atharvashiras, after describing the universal form of rudra, provides a verse corresponding to the famous R^ik RV 8.48.3, thereby connecting amR^ita and rudra:
apAma somam amR^itA abhUma+
aganma jyotir avidAma devAn | kiM nUnam asmAn kR^iNavad arAtiH
kim u dhUrtir amR^itam mArtyasya ||
The bhairava-srotas specifies a tAntrika mantra to amR^itarudra:
OM hrIM vaM ThaM amR^itarudrAya AM hrIM kroM pratikUlaM me nashyatv anukUlaM me vashamAnaya svAhA ||
The same is also found in the shrIkula aligned tantra, the vA~ncha-kalpa-latA, where amR^itarudra is a prominent deity.
The kAma-ratna, a mantra compendium, specifies a distinct amR^itarudra mantra:
OM namo bhagavate rudrAya amR^itArka-madhye saMsthitAya
mama sharIre amR^itaM kuru kuru saH svAhA ||
The pUrvAmnAya tantra, the mAlinIvijaya(uttara) specifies that there are 16 amR^ita-rudra-s corresponding to the 16 vowels of the Sanskrit language. It gives their names thus:
amR^ito .amR^itapUrNash cha amR^itAbho.amR^itadravaH |
amR^itaugho .amR^itormish cha amR^itasyandano .aparaH ||
amR^itA~Ngo .amR^itavapur amR^itodgAra eva cha |
amR^itAsyo .amR^itatanus tathA chAmR^itasechanaH | | tan mUrtir amR^iteshash cha sarvAmR^itadharo .aparaH |
ShoDashaite samAkhyAtA rudra-bIja-samudbhavAH ||
Here, the rudra-bIja-s are the svara-s (vowels): the 14 found in the bhinnayoni-vidyA +aM and aH ( TW).
In the Ishvara-pratyabhij~nAvivR^iti-vimarshinI, his commentary on utpaladeva’s work, abhinavagupta composes one verse for each amR^ita-rudra at the beginning of each chapter.
Taken together, this stotra of 16 verses is used by the Kashmirians in the devotional worship of the 16 amR^itarudra-s. Their basic mantra is the praNava followed by the svara-bIja with their respective names.
We posit that the tradition of the amR^itarudra-s and that of amR^iteshvara-bhairava of the netra tantra tradition had a common origin, probably in the ancient matrix of ideas like that presented in chapter 3 of the atharvashiras and the mR^itasaMjivanI-R^ik.
However, the two represent distinct evolutes centered on three different mantra traditions: one on the path leading to the netra tradition (the tripartite mR^ityu~njaya) and two via the bhairavasrotas (the singular amR^itarudra mantra) and its successor tradition, the pUrvAmnAya (the 16 amR^itarudra-s). Both the netra tradition and the singular amR^itarudra also secondarily interacted with both the pUrvAmnAya and dakShiNAmnAya.