We investigate arithmetic properties of an overpartition counting function that first
arose in connection with Schur’s partition theorem and a universal mock theta function.
Motivated by work of Basil Gordon on the Rogers–Ramanujan identities, we first give a
complete characterization of the parity of this overpartition function in the progressions
,
, and
in terms of the
factorization of
for certain
and
.
We then find similar characterizations of the residue modulo
in the
progressions
and
.
Finally, we prove some Ramanujan-type congruences modulo
. Our
proofs use basic facts about modular forms and some elementary algebraic number
theory.
PDF Access Denied
We have not been able to recognize your IP address
18.212.102.174
as that of a subscriber to this journal.
Online access to the content of recent issues is by
subscription, or purchase of single articles.
Please contact your institution's librarian suggesting a subscription, for example by using our
journal-recommendation form.
Or, visit our
subscription page
for instructions on purchasing a subscription.