TY - JOUR
T1 - Dissections of Strange q-Series
AU - Ahlgren, Scott
AU - Kim, Byungchan
AU - Lovejoy, Jeremy
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2019/11/1
Y1 - 2019/11/1
N2 - In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontsevich–Zagier series are divisible by a certain q-factorial. This was proved by the first two authors. In this paper, we extend this strong divisibility property to two generic families of q-hypergeometric series which, like the Kontsevich–Zagier series, agree asymptotically with partial theta functions.
AB - In a study of congruences for the Fishburn numbers, Andrews and Sellers observed empirically that certain polynomials appearing in the dissections of the partial sums of the Kontsevich–Zagier series are divisible by a certain q-factorial. This was proved by the first two authors. In this paper, we extend this strong divisibility property to two generic families of q-hypergeometric series which, like the Kontsevich–Zagier series, agree asymptotically with partial theta functions.
KW - Congruences
KW - Fishburn numbers
KW - Kontsevich–Zagier strange function
KW - Partial theta functions
KW - q-Series
UR - http://www.scopus.com/inward/record.url?scp=85074618410&partnerID=8YFLogxK
U2 - 10.1007/s00026-019-00447-6
DO - 10.1007/s00026-019-00447-6
M3 - Article
AN - SCOPUS:85074618410
SN - 0218-0006
VL - 23
SP - 427
EP - 442
JO - Annals of Combinatorics
JF - Annals of Combinatorics
IS - 3-4
ER -