A sufficient condition for the convergence of a generalized formal power series solution to an algebraic q-difference equation is provided. The main result leans on a geometric property related to the semi-group of (complex) power exponents of such a series. This property corresponds to the situation in which the small divisors phenomenon does not arise. Some examples illustrating the cases where the obtained sufficient condition can or cannot be applied are also depicted.

中文翻译：

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关于q-差分方程广义幂级数解的收敛性

提供了代数q差分方程的广义形式幂级数解收敛的充分条件。主要结果依赖于与此类系列的（复）幂指数的半群相关的几何特性。该性质对应于不出现小除数现象的情况。还描述了一些示例，说明了所获得的充分条件可以或不可以应用的情况。