Algebraic relations among solutions of linear differential equations

Author:
Michael F. Singer

Journal:
Trans. Amer. Math. Soc. **295** (1986), 753-763

MSC:
Primary 12H05; Secondary 34A20

MathSciNet review:
833707

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Abstract: Using power series methods, Harris and Sibuya [**3,4**] recently showed that if is an ordinary differential field of characteristic zero and is an element of a differential extension of such that and satisfy linear differential equations with coefficients in , then is algebraic over . Using differential galois theory, we generalize this and characterize those polynomial relations among solutions of linear differential equations that force these solutions to have algebraic logarithmic derivatives. We also show that if is an algebraic function of genus and if and or and satisfy linear differential equations, then is an algebraic function.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1986-0833707-X

Keywords:
Linear differential equations,
Picard-Vessiot theory,
linear algebraic groups

Article copyright:
© Copyright 1986
American Mathematical Society