Akṣayatṛitīyā (akshayatritiya) is the third day of the bright fortnight in the month of Vaiśākha (Vaishakha) of the Hindu calendar. It is said that on this day goddess Gaṅgā (Ganga) was born in a four-armed form in the abode of Himālaya (Himalaya; the river Ganga has her source in the Himalayas). According to Purāṇas (Puranas), this lunar day is also known as satyayugādyā (satyayugadya), i.e., the lunar day marking the beginning of Satyayuga (Satyayuga)— purāṇe kathitā yā ca yugādyā prathamā sakhi.
All activities performed on this day, including charities, fire oblation ceremonies, meditating on incantations, etc., contribute to the attainment of eternal puṇya (punya; virtue). This third lunar day becomes even more auspicious and commendable [for customs and rituals] if the timing of the star (nakṣatra; nakshatra) Kṛttikā (Krittika) is conjoined. The customs prescribed for this lunar day include fasting and worshiping Srīhari (Srihari) of Viṣṇu (Vishnu).
It is chronicled that on this lunar day of akṣayatṛitīyā, Paraśurāma (Parashurama), the sixth incarnation of Srīhari, was born. Kamalākara Bhaṭṭa (Kamalakar Bhatta), in his smṛti (smriti) book called Nirṇayasindhu (Nirnayasindhu), cites from Bhārgavārcanadīpikā (Bhargavachanadipika), an even more ancient smṛti (smriti) text, which in turn refers to Skandapurāṇa (Skandapurana) and Bhaviṣyapurāṇa (Bhavishyapurana). Bhaṭṭa quotes from here that Paraśurāma was born in the evening of the third lunar day of the bright fortnight in the month of Vaiśākha, i.e, on the night of akṣayatṛitīyā, under Punarvasu nakṣatra. At the time of his birth, six planets were exalted and Rāhu (Rahu; the north node of the moon) was in Mithuna (Gemini). In such a remarkable astrological scenario Srīhari was born as ‘Rāma’ (Rama) to Reṇukā (Renuka). Therefore this day is also known as Paraśurāmajayantī (Parashuramajayanti) or Paraśurāma’s birth anniversary—
vaiśakhasya site pakṣe tṛtīyāyāṃ punarvasau
niśāyāḥ prathame yāme rāmākhyaḥ samaye hariḥ.
soccagaiḥ ṣaṭgrahairyukte mithune rāhusaṃsthite
reṇukāyāstu yo garbhādavatīrṇo hariḥ svayam.