On q-algebraic equations and their power series solutions
arXiv:1311.5549
Abstract
We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case where the solution is divergent, giving a sharp estimate on the growth of the coefficients. As a consequence, we obtain a bound on the q-Gevrey order of the formal solution, which is optimal in some cases. Various examples illustrate our main results.
53 pages, 1 figure. Theorem 2.3.4 in the previous version was wrong and is not in this version