Extensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms
| dc.creator | Srinivasan, V. Ravi | |
| dc.date | 2008-11-18 | |
| dc.date.accessioned | 2026-07-07T10:19:25Z | |
| dc.date.available | 2026-07-07T10:19:25Z | |
| dc.description | Let F be a characteristic zero differential field with an algebraically closed field of constants, E be a no-new-constant extension of F by antiderivatives of F and let y1, ..., yn be antiderivatives of E. The antiderivatives y1, ..., yn of E are called J-I-E antiderivatives if the derivatives of yi in E satisfies certain conditions. We will discuss a new proof for the Kolchin-Ostrowski theorem and generalize this theorem for a tower of extensions by J-I-E antiderivatives and use this generalized version of the theorem to classify the finitely differentially generated subfields of this tower. In the process, we will show that the J-I-E antiderivatives are algebraically independent over the ground differential field. An example of a J-I-E tower is extensions by iterated logarithms. We will discuss the normality of extensions by iterated logarithms and produce an algorithm to compute its finitely differentially generated subfields. | |
| dc.description | 66 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0811.3004 | |
| dc.identifier | http://arxiv.org/abs/0811.3004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174499 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Commutative Algebra | |
| dc.subject | 12H05, 12Fxx | |
| dc.title | Extensions by Antiderivatives, Exponentials of Integrals and by Iterated Logarithms | |
| dc.type | text |