$q$-Borel-Laplace summation for $q$-difference equations with two slopes

Abstract

In this paper, we consider linear $q$-difference systems with coefficients that are germs of meromorphic functions, with Newton polygon that has two slopes. Then, we explain how to compute similar meromorphic gauge transformations than those appearing in the work of Bugeaud, using a $q$-analogue of the Borel-Laplace summation.

The final version of this paper will be published in Journal of Difference Equations and Applications

References in corpus (3)

• Building meromorphic solutions of $q$-difference equations using a Borel-Laplace summation
• The q-analogue of the wild fundamental group (II)
• Galois theory of q-difference equations

Cited by in corpus (4)

• On the multiple-scale analysis for some linear partial $q$-difference and differential equations with holomorphic coefficients
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• Théorie analytique locale des équations aux $q$-différences de pentes arbitraires
• The $q$-Borel Sum of Divergent Basic Hypergeometric Series ${}_r{\phi }_s(a;b;q,x)$