Ramanujan's theta functions and parity of parts and cranks of partitions
Sprache des Titels:
Englisch
Original Kurzfassung:
In this paper we explore intricate connections between Ramanujan's theta functions and a class of partition functions defined by the nature of the parity of their parts. This consequently leads us to the parity analysis of the crank of a partition and its correlation to the number of partitions with odd number of parts, self-conjugate partitions, and also with Durfee squares and Frobenius symbols.
Forschungs-