Desingularization of First Order Linear Difference Systems with Rational Function Coefficients [article]

Moulay A. Barkatou, Maximilian Jaroschek
<span title="2018-02-04">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
It is well known that for a first order system of linear difference equations with rational function coefficients, a solution that is holomorphic in some left half plane can be analytically continued to a meromorphic solution in the whole complex plane. The poles stem from the singularities of the rational function coefficients of the system. Just as for differential equations, not all of these singularities necessarily lead to poles in solutions, as they might be what is called removable. In
more &raquo; ... r work, we show how to detect and remove these singularities and further study the connection between poles of solutions and removable singularities. We describe two algorithms to (partially) desingularize a given difference system and present a characterization of removable singularities in terms of shifts of the original system.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.01150v1">arXiv:1802.01150v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/zkf2kiidovhtrfie2htsvnnnbe">fatcat:zkf2kiidovhtrfie2htsvnnnbe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200911125500/https://arxiv.org/pdf/1802.01150v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/6d/30/6d305d9857b38bb35cfd5b174b5c1066ba26c52c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1802.01150v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>