10.46298/hrj.2022.8930
https://hrj.episciences.org/8930
Lovejoy, Jeremy
Jeremy
Lovejoy
Quantum q-series identities
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 Bryson-Ono-Pitman-Rhoades and Folsom-Ki-Vu-Yang. 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.
episciences.org
$q$-series identities
Ramanujan
2010 Mathematics Subject classification: 33D15
[MATH]Mathematics [math]
2022-01-09
2022-01-09
2022-01-09
en
journal article
https://hal.archives-ouvertes.fr/hal-03498183v1
2804-7370
https://hrj.episciences.org/8930/pdf
VoR
application/pdf
Hardy-Ramanujan Journal
Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021
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