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On Some Partition Functions Related to Some Mock Theta Functions

100%

Patkowski A.

Bulletin of the Polish Academy of Sciences. Mathematics

2009

tom 57

nr 1

1-8

We show that some partitions related to two of Ramanujan's mock theta functions are related to indefinite quadratic forms and real quadratic fields. In particular, we examine a third order mock theta function and a fifth order mock theta function.

Another smallest part function related to Andrews' spt function

100%

Patkowski A.

nr 2

101-105

We offer some relations and congruences for two interesting spt-type functions, which together form a relation to Andrews' spt function.

Divisors, partitions and some new q-series identities

100%

Patkowski A.

Colloquium Mathematicum

2009

tom 117

nr 2

289-294

We obtain new q-series identities that have interesting interpretations in terms of divisors and partitions. We present a proof of a theorem of Z. B. Wang, R. Fokkink, and W. Fokkink, which follows as a corollary to our main q-series identity, and offer a similar result.