episciences.org_8930_1653160210
1653160210
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
HardyRamanujan Journal
28047370
10.46298/journals/hrj
https://hrj.episciences.org
01
09
2022
Volume 44  Special...
Quantum qseries identities
Jeremy
Lovejoy
As analytic statements, classical $q$series identities are equalities between power series for $q<1$. This paper concerns a different kind of identity, which we call a quantum $q$series identity. By a quantum $q$series identity we mean an identity which does not hold as an equality between power series inside the unit disk in the classical sense, but does hold on a dense subset of the boundary  namely, at roots of unity. Prototypical examples were given over thirty years ago by Cohen and more recently by BrysonOnoPitmanRhoades and FolsomKiVuYang. We show how these and numerous other quantum $q$series identities can all be easily deduced from one simple classical $q$series transformation. We then use other results from the theory of $q$hypergeometric series to find many more such identities. Some of these involve Ramanujan's false theta functions and/or mock theta functions.
01
09
2022
8930
https://hal.archivesouvertes.fr/hal03498183v1
10.46298/hrj.2022.8930
https://hrj.episciences.org/8930

https://hrj.episciences.org/8930/pdf