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

The \(\exp _q(z)\) 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 \(\exp _q\). After proving some simpler but new relations for it, we make a complete description of the inverse map of \(\exp _q(z)\), including its branch structure and Riemann surface.