, Volume 40, Issue 1, pp 6777
First online:
Algebraic independence of elementary functions and its application to Masser's vanishing theorem
 Keiji NishiokaAffiliated withDepartment of Mathematics, Nara Women's University
 , Kumiko NishiokaAffiliated withDepartment of Mathematics, Nara Women's University
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To prove this, the following fact on elementary functions will be needed: LetK be an ordinary differential field andC be its field of constants. LetR be a differential field extension ofK andu _{1},⋯,u _{ m } be elements ofR such that the field of constants ofR is the same asC and for eachi the field extensionK _{ i } =K(u _{1},⋯,u _{ i }) ofK is a differential one such thatu′_{ i } =t′_{ i−1} u _{ i } for somet _{ i−1}∈K _{ i−1} oru _{ i } is algebraic overK _{ i−1}. Letf _{1},⋯,f _{ n } ∈R be distinct elements moduloC and suppose that for eachi there is a nonzeroe _{ i } ∈R withe′ _{ i } =f′ _{ i } e _{ i }. Thene _{1},⋯,e _{ n } are linearly independent overK.
AMS (1980) subject classification
Primary 11J81 Secondary 12H05 Title
 Algebraic independence of elementary functions and its application to Masser's vanishing theorem
 Journal

aequationes mathematicae
Volume 40, Issue 1 , pp 6777
 Cover Date
 199012
 DOI
 10.1007/BF02112281
 Print ISSN
 00019054
 Online ISSN
 14208903
 Publisher
 BirkhäuserVerlag
 Additional Links
 Topics
 Keywords

 Primary 11J81
 Secondary 12H05
 Industry Sectors
 Authors

 Keiji Nishioka ^{(1)} ^{(2)}
 Kumiko Nishioka ^{(1)} ^{(2)}
 Author Affiliations

 1. Takabatakecho 184632, 630, Nara, Japan
 2. Department of Mathematics, Nara Women's University, KitaUoya Nishimachi, 630, Nara, Japan