David MetacarpaAffiliation: Amherst College Title Of Talk: Antiquantum $q$-series identities and mock theta functions
URLS: Abstract: Ramanujan's original definition of mock theta functions from 1920 involves their asymptotic behaviors at roots of unity on the boundary of the disk of convergence $|q|<1$. One question of interest to us is: do $q$-series identities involving the mock theta functions still hold at roots of unity? Inspired by Lovejoy's work on quantum $q$-series identities, we explore antiquantum $q$-series identities, or identities between series which are equal inside the disk $|q|<1$ but which hold at dense sets of roots of unity on the boundary for which one of the series diverges and is unnaturally truncated. In this talk, we will establish antiquantum $q$-series identities for all of Ramanujan's third order mock theta functions. This talk comes from joint work with Amanda Folsom (Amherst College).
WARNING: This page contains MATH-JAX
Last update made Tue Mar 10 21:28:04 CDT 2026.
|