2024/02/18 by Jeremy Lovejoy, Lovejoy, Jeremy, Rishabh Sarma +1
Mathematics · #33D15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2402.11529
openalex publication_date 2024/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
In the first part of this paper we prove a conjecture of Hikami on the values of the radial limits of a family of q-hypergeometric false theta functions. Hikami conjectured that the radial limits are obtained by evaluating a truncated version of the series. He proved a special case of his conjecture by computing the Kashaev invariant of certain torus links in two different ways. We prove the full conjecture using Bailey pairs. In the second part of the paper we show how the framework of Bailey pairs leads to further results of this type.