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Algebraic independence of values of hypergeometricE-functions

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References

  1. C. L. Siegel,Transcendental Numbers, Princeton Univ. Press, Princeton (1949).

    Google Scholar 

  2. A. B. Shidlovskii,Transcendental Numbers [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  3. F. Beukers, W. D. Brownawell, and G. Hekman, “Siegel normality,”Ann. Math.,127, 297–308 (1988).

    Google Scholar 

  4. F. Beukers, “Some new results on algebraic independence ofE-functions,” in:New Advances in Transcendence Theory, Cambridge Univ. Press (1988), pp. 56–67.

  5. V. Kh. Salikhov, “Formal solutions of linear differential equations and their applications in the theory of transcendental numbers,”Tr. Mosk. Mat. Obshch.,51, 223–256 (1988).

    MATH  Google Scholar 

  6. V. Kh. Salikhov, “Irreducibility of hypergeometric equations and algebraic independence ofE-functions,”Acta Arith.,53, No. 5, 453–471 (1990).

    MATH  MathSciNet  Google Scholar 

  7. Yu. V. Nesterenko, “Algebraic independence of the values ofE-functions satisfying inhomogeneous linear differential equations,”Mat. Zametki,5, No. 5, 587–598 (1969).

    MATH  MathSciNet  Google Scholar 

  8. M. A. Cherepnev, “Algebraic independence of some subclasses of hypergeometric functions,”Mat. Zametki,55, No. 1, 117–129 (1994).

    MATH  MathSciNet  Google Scholar 

  9. S. Lang,Algebra [Russian translation], Mir, Moscow (1968).

    Google Scholar 

  10. V. Kh. Salikhov, “A test for algebraic independence of the values of one class of hypergeometricE-functions,”Mat. Sb.,181, No. 2, 189–212 (1990).

    Google Scholar 

  11. I. Kaplansky,An Introduction to Differential Algebra, Hermann, Paris (1957).

    Google Scholar 

  12. M. A. Cherepnev, “Algebraic independence of the values of hypergeometricE-functions,”Usp. Mat. Nauk, No. 6, 149–150 (1990).

    Google Scholar 

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Authors and Affiliations

  1. Moscow State University, USSR

    M. A. Cherepnev

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  1. M. A. Cherepnev
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Additional information

This work was supported by ISF Grant No. NTN000.

Translated from Matematicheskie Zametki, Vol. 57, No. 6, pp. 896–912, June, 1995.

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Cherepnev, M.A. Algebraic independence of values of hypergeometricE-functions. Math Notes 57, 630–642 (1995). https://doi.org/10.1007/BF02304559

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