M. S. Mahadeva Naika

A continued fraction of order twelve

In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.

Arithmetic properties of 5-regular bipartitions

Let Bt(n) denote the number of t-regular bipartitions of n. In this work, we establish several infinite families of congruences modulo powers of 2 and 5 for B5(n). For example, we find that for all nonnegative integers n, i and j and r ∈{23, 47}, B5 22i+4 ⋅ 52j+1n + r ⋅ 22i+1 ⋅ 52j − 1 3 ≡ 0(mod24).

Congruences for Andrews singular overpartition pairs

Andrews defined the combinatorial objects called singular overpartitions denoted by C¯k,i(n), which counts the number of overpartitions of n in which no part is divisible by k and only parts ≡±i(modk) may be overlined. In this paper, we investigate the arithmetic properties of Andrews singular overpartition pairs. Let A¯i,jδ(n) be the number of overpartition pairs of n in which no part is divisible by δ and only parts ≡±i,±j(modδ) may be overlined. We will prove a number of Ramanujan like congruences and infinite families of congruences for A¯1,26(n) modulo 3, 9, 18 and 36, infinite families of congruences for A¯2,48(n) modulo 4 and 8, infinite families of congruences for A¯1,512(n) modulo 6 and 9.

Congruences modulo \(2\) for certain partition functions

Let

On some new general theorems for the explicit evaluations of Ramanujan’s remarkable product of theta-functions

b_{3,5}(n)

Congruences for Andrews' singular overpartitions

denote the number of partitions of

Color Partition Identities Arising from Ramanujan’s Theta-Functions

n

Arithmetic properties arising from Ramanujan’s theta functions

into parts that are not multiples of 3 or 5. We establish several infinite families of congruences modulo 2 for

On some new P–Q mixed modular equations

b_{3,5}(n)

On 3-regular partitions with odd parts distinct

. In the process, we also prove numerous parity results for broken 7-diamond partitions.