Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


The $ n$th roots of solutions of linear ordinary differential equations

Authors: William A. Harris and Yasutaka Sibuya
Journal: Proc. Amer. Math. Soc. 97 (1986), 207-211
MSC: Primary 12H05; Secondary 34A30
MathSciNet review: 835866
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we shall prove the following theorem: Let $ K$ be a differential field of characteristic zero. Let $ \varphi $ and $ \psi $ be elements of a differential field extension of $ K$ such that (i) $ \varphi \ne 0$ and $ \psi \ne 0$; (ii) $ \varphi $ and $ \psi $ satisfy nontrivial linear differential equations with coefficients in $ K$, say, $ P(\varphi ) = 0$ and $ Q(\psi ) = 0$; (iii) $ \varphi = {\psi ^n}$ for some positive integer $ n$ such that $ n \geqslant {\text{ ord }}P$. Then the logarithmic derivatives of $ \varphi $ and $ \psi $ are algebraic over $ K$. (Note that $ \varphi '/\varphi = n(\psi '/\psi )$.)

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12H05, 34A30

Retrieve articles in all journals with MSC: 12H05, 34A30

Additional Information

PII: S 0002-9939(1986)0835866-7
Article copyright: © Copyright 1986 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia