Details:
| Title | Logarithmic derivatives of solutions to linear differential equations | | Author(s) | Christopher Hillar | | Type | Article in Journal | | Abstract | 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 Gr\"{o}bner
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. | | Keywords | logarithmic derivative, linear differential equation, differential field, Gr\"{o}bner basis | | Length | 9 |
| File |
| | URL |
http://arxiv.org/abs/math.AG/0309124 |
| Language | English | | Journal | Proc. Amer. Math. Soc. | | Volume | 132 | | Number | 9 | | Pages | 2693-2701 | | Year | 2004 | | Edition | 0 | | Translation |
No | | Refereed |
Yes | | Organization |
Texas A&M University | | Sponsors | Texas A&M | | Conferencename | Christopher Hillar |
|
