Liuquan Wang

Arithmetic identities and congruences for partition triples with 3-cores

Let

Arithmetic properties of partition triples with odd parts distinct

{{B}_{3}}(n)

Arithmetic properties of partition quadruples with odd parts distinct

denote the number of partition triples of

New proofs of Ramanujan’s identities on false theta functions

n

Arithmetic properties of overpartition triples

where each partition is 3-core. With the help of generating function manipulations, we find several infinite families of arithmetic identities and congruences for

A curious congruence modulo prime powers

{{B}_{3}}(n)

New congruences for partitions related to mock theta functions

. Moreover, let

A new curious congruence involving multiple harmonic sums

\omega (n)

Explicit formulas for partition pairs and triples with 3-cores

denote the number of representations of a nonnegative integer

A Curious Congruence Involving Alternating Harmonic Sums

n