2008/11/18 by Varadharajan Srinivasan, V. Ravi Srinivasan, Srinivasan, V. Ravi · 3 citations
Mathematics · #12Fxx #12H05 #Classical Analysis and ODEs (math.CA) #Commutative Algebra (math.AC) #FOS: Mathematics #History and Theory of Mathematics #Iterative Methods for Nonlinear Equations #Mathematical and Theoretical Analysis #math.AC #math.CA #msc:12Fxx #msc:12H05
paper · pdf · doi:10.48550/arxiv.0811.3004
66 pages, 1 figure
arxiv created 2008/11/18 · openalex publication_date 2008/11/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.