The Riemann surface of the inverse of Jackson’s q-exponential function

The \(\exp _q(z)\) ${exp}_q(z)$ function is the standard q-analogue of the exponential. Since not much is known about this function, our aim is to give a contribution to the knowledge on \(\exp _q\) ${exp}_q$ . After proving some simpler but new relations for it, we make a complete description of the inverse map of \(\exp _q(z)\) ${exp}_q(z)$ , including its branch structure and Riemann surface.