Logarithmic Derivatives of Solutions to Linear Differential Equations
| dc.creator | Hillar, Christopher J. | |
| dc.date | 2003-09-07 | |
| dc.date | 2003-10-21 | |
| dc.date.accessioned | 2026-07-07T05:00:56Z | |
| dc.date.available | 2026-07-07T05:00:56Z | |
| dc.description | Given an ordinary differential field $K$ of characteristic zero, it is known that if $y$ and $1/y$ satisfy linear differential equations with coefficients in $K$, then $y'/y$ is algebraic over $K$. We present a new short proof of this fact using Gröbner basis techniques and give a direct method for finding a polynomial over $K$ that $y'/y$ satisfies. Moreover, we provide explicit degree bounds and extend the result to fields with positive characteristic. Finally, we give an application of our method to a class of nonlinear differential equations. | |
| dc.description | 9 pages, Proceedings of the AMS | |
| dc.identifier | https://arxiv.org/abs/math/0309124 | |
| dc.identifier | http://arxiv.org/abs/math/0309124 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68500 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | 34M15 13P10 (Primary), 34A26 (Secondary) | |
| dc.title | Logarithmic Derivatives of Solutions to Linear Differential Equations | |
| dc.type | text |