PreprintarXiv licencearXiv
On convergence of formal Dulac series, satisfying an algebraic q-difference equation
Abstract
An algebraic q-difference equation for |q|>1 is considered. A sufficient condition is proposed for the convergence of a solution to such an equation in the form of a Dulac series within a sector centered at the origin. An example illustrating the application of this sufficient condition is provided.
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BibTeX
@misc{gaianov2026convergence,
title = {{On convergence of formal Dulac series, satisfying an algebraic $q$-difference equation}},
author = {Nikita V. Gaianov and Anastasia V. Parusnikova},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31322},
eprint = {2609.31322},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31322},
}
RIS
TY - UNPB
TI - On convergence of formal Dulac series, satisfying an algebraic q-difference equation
AU - Nikita V. Gaianov
AU - Anastasia V. Parusnikova
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31322
UR - https://arxiv.org/abs/2609.31322
AB - An algebraic q-difference equation for |q|>1 is considered. A sufficient condition is proposed for the convergence of a solution to such an equation in the form of a Dulac series within a sector centered at the origin. An example illustrating the application of this sufficient condition is provided.
ER -