{"docId":8930,"paperId":8930,"url":"https:\/\/hrj.episciences.org\/8930","doi":"10.46298\/hrj.2022.8930","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[{"vid":607,"name":"Volume 44 - Special Commemorative volume in honour of Srinivasa Ramanujan - 2021"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-03498183","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-03498183v1","dateSubmitted":"2022-01-06 21:03:28","dateAccepted":"2022-01-09 18:17:30","datePublished":"2022-01-09 18:18:00","titles":{"en":"Quantum q-series identities"},"authors":["Lovejoy, Jeremy"],"abstracts":{"en":"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."},"keywords":[{"en":"$q$-series identities"},{"en":"Ramanujan"},"2010 Mathematics Subject classification: 33D15","[MATH]Mathematics [math]"]}