On the functional equation Af2 + Bg2 = 1 on the field of complex p-adic numbers

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Abstract

For a fixed prime p, let Cp denote the complex p-adic numbers. For polynomials A, B ε C p [x] we consider decompositions A (x) f2 (x) + B (x) g2 (x) = 1 of entire functions f, g on C p and try to improve an impossibility result due to A. Boutabaa concerning transcendental f, g. We also provide a new proof of a p-adic diophantic statement due to D. N. Clark, which is an important ingredient of Boutabaa’s method.

Original languageEnglish
Pages (from-to)68-76
Number of pages9
JournalP-Adic Numbers, Ultrametric Analysis, and Applications
Volume2
Issue number1
DOIs
Publication statusPublished - 1 Jan 2010
Externally publishedYes

Keywords

  • p-adic analysis
  • p-adic differential equations
  • p-adic functional equations

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