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Rational approximation to solutions of linear differential equations with algebraic coefficients
| Content Provider | Semantic Scholar |
|---|---|
| Author | Schmidt, Wolfgang M. |
| Copyright Year | 1975 |
| Abstract | ILet K be the field of formal series a= a + a + a t1 +... and let be the valuation with |a 2k if ak 0 -1 C I2i k 0. Suppose a e K satisfies an mth order linear differential equation whose coefficients are algebraic functions of t. Then for E > 0 there are only finitely many rational functions p(t)/q(t) with I a p(t)/q(t)| 0, then there are at most finitely many rational functions p(t)/q(t) with la (p(t)/q(t))| 0, at most finitely many rational functions p(t)/q(t) satisfy (3) |X -(p(t)/q(t))| 0. The proof of the theorem will depend on a power series version of my generalization [31, [41 of Roth's theorem to simultaneous approximation. The same Received by the editors September 13, 1974. AMS (MOS) subject classifications (1970). Primary 10F45; Secondary 10F25. 1 Written with partial support from NSF grant NSF-GP-33026X. Copyright ( 1975, American Mathematical Society 285 This content downloaded from 157.55.39.176 on Sat, 09 Apr 2016 06:30:13 UTC All use subject to http://about.jstor.org/terms |
| Starting Page | 285 |
| Ending Page | 289 |
| Page Count | 5 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-1975-0387210-2 |
| Volume Number | 53 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1975-053-02/S0002-9939-1975-0387210-2/S0002-9939-1975-0387210-2.pdf |
| Alternate Webpage(s) | https://www.ams.org/journals/proc/1975-053-02/S0002-9939-1975-0387210-2/S0002-9939-1975-0387210-2.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1975-0387210-2 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
