Transformation Formula of the "2nd" Order Mock Theta Function

TL;DR

This paper derives a transformation formula for the second order mock theta function, linking it to quantum invariants of Seifert manifolds, advancing understanding in the intersection of mock theta functions and quantum topology.

Contribution

It provides a new transformation formula for the second order mock theta function, connecting it with quantum invariants of Seifert manifolds, which was not previously established.

Findings

Derived a transformation formula for the 2nd order mock theta function

Connected mock theta functions with quantum invariants of Seifert manifolds

Enhanced understanding of the relationship between mock theta functions and quantum topology

Abstract

We give a transformation formula for the ``2nd order'' mock theta function which was recently proposed in connection with the quantum invariant for the Seifert manifold.