November 30, 2025Open Access

Bailey pairs and quantum q-series identities. I. The classical identities

Puntos clave

Quadratic forms play a crucial role in proving q-series identities, highlighting their mathematical relevance.
The analysis specifically demonstrates relationships at roots of unity through established identities and lemmas.
Approach utilizing Bailey pairs and changes-of-base enhances the derivation of identities in this context.
Findings emphasize further exploration of Bailey pairs within the realm of infinite families and mock theta functions.

Resumen

Abstract We use Bailey pairs to prove q -series identities at roots of unity due to Cohen and Bryson–Ono–Pitman–Rhoades. The proofs use Bailey pairs with quadratic forms developed in the study of mock theta functions. In addition to the standard Bailey lemma, we require some changes-of-base established by Bressoud–Ismail–Stanton. We then embed the identities in infinite families using the Bailey chain.

Leer artículo completoexternamente

Me gusta

Guardar

Ver artículo completo