TY - JOUR
T1 - Odd-balanced unimodal sequences and related functions
T2 - Parity, mock modularity and quantum modularity
AU - Kim, Byungchan
AU - Lim, Subong
AU - Lovejoy, Jeremy
N1 - Publisher Copyright:
© 2016 American Mathematical Society.
PY - 2016
Y1 - 2016
N2 - We define odd-balanced unimodal sequences and show that their generating function V(x, q) has the same remarkable features as the generating function for strongly unimodal sequences U(x, q). In particular, we discuss (mixed) mock modularity, quantum modularity, and congruences modulo 2 and 4. We also study two related functions which share some of the properties of U(x, q) and V(x, q).
AB - We define odd-balanced unimodal sequences and show that their generating function V(x, q) has the same remarkable features as the generating function for strongly unimodal sequences U(x, q). In particular, we discuss (mixed) mock modularity, quantum modularity, and congruences modulo 2 and 4. We also study two related functions which share some of the properties of U(x, q) and V(x, q).
KW - Congruences
KW - Mock theta functions
KW - Quantum modular forms
KW - Rank
KW - Unimodal sequences
UR - http://www.scopus.com/inward/record.url?scp=84975127356&partnerID=8YFLogxK
U2 - 10.1090/proc/13027
DO - 10.1090/proc/13027
M3 - Article
AN - SCOPUS:84975127356
SN - 0002-9939
VL - 144
SP - 3687
EP - 3700
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 9
ER -