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Arithmetically independent integers and values of rational functions

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Abstract

We prove the existence of arithmetically independent integers and their properties and apply them to values of rational functions on algebraic varieties.

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References

  1. Hartshorne, R.: Algebraic Geometry. Springer-Verlag 1977

  2. Nagell, T.: Introduction to Number Theory. New York and Stockholm: John Wiley and Sons 1951

    MATH  Google Scholar 

  3. Robinson, A.: Non-standard Analysis. Amsterdam: North-Holland 1966.

    MATH  Google Scholar 

  4. Robinson, A. and Roquette, P.: On the finiteness theorem of Siegel and Mahler concerning diophantine equation. J. Number Theory7, 121–176 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  5. Yasumoto, M.: Nonstandard arithmetic of function fields over H-convex subfields of*ℚ. j. Reine Angew. Math.342, 1–11 (1983)

    MATH  MathSciNet  Google Scholar 

  6. Yasumoto, M.: Nonstandard arithmetic of Hilbert subsets. Annals of pure and applied Logic52, 195–202 (1991)

    Article  MathSciNet  Google Scholar 

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Yasumoto, M. Arithmetically independent integers and values of rational functions. Manuscripta Math 85, 1–10 (1994). https://doi.org/10.1007/BF02568179

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  • DOI: https://doi.org/10.1007/BF02568179

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