On q-algebraic equations and their power series solutions

2013/11/21 by Barbe, Ph., McCormick, W. P. · 1 citation
#05A16 #05A30 #33E99 #39A13 #41A60 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/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.

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