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On linear independence of the values of entire hypergeometric functions with irrational parameters

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References

  1. A. B. Shidlovskiî, Diophantine Approximations and Transcendental Numbers [in Russian], Izdat. Moscow Univ., Moscow (1982).

    Google Scholar 

  2. A. I. Galochkin, “On some analog of Siegel's method,” Vestnik Moscow Univ. Ser. I Mat., Mekh., No. 2, 30–34 (1986).

    Google Scholar 

  3. G. V. Chudnovsky, “Padé approximations to the generalized hypergeometric functions. I,” J. Math. Pures Appl. (9),58, No. 4, 445–476 (1979).

    Google Scholar 

  4. G. V. Chudnovsky, “On application of diophantine approximations (G-functions, Padé approximation),” Proc. Nat. Acad. Sci. USA,81, 1926–1930 (1984).

    Google Scholar 

  5. D. V. Chudnovsky and G. V. Chudnovsky, “Applications of Padé approximation to diophantine inequalities in values ofG-functions,” Lecture Notes in Math.,1135, 9–51 (1985).

    Google Scholar 

  6. A. I. Galochkin, “On effective bounds for certain linear forms,” in: New Advances in Transcendence Theory, Cambridge, New Rochell, Melburne, Cambridge Univ., Sydney, 1988, pp. 207–215.

    Google Scholar 

  7. A. I. Galochkin, “Effective bounds for certain linear forms,” in: Abstracts: All-Union Conference “Number Theory and Its Applications,” Tbilisi, 1985, pp. 39–40.

  8. P. L. Ivankov, “Simultaneous approximations of value of some entire functions by numbers belonging to a cubic field,” Vestnik Moscow Univ. Ser. I Mat. Mekh., No.3, 53–56 (1987).

    Google Scholar 

  9. C. Osgood, “Some theorems on diophantine approximations,” Trans. Amer. Math. Soc.,123, 64–87 (1966).

    Google Scholar 

  10. A. I. Galochkin, “Arithmetic properties of the values of certain entire hypergeometric functions,” Sibirsk. Mat. Zh.,17, No. 6, 1220–1235 (1976).

    Google Scholar 

  11. A. I. Galochkin, “Arithmetic properties of the values ofG-functions,” in: Abstracts: All-Union School “Constructive Methods and Algorithms of Number Theory,” Minsk, 1989, p. 34.

  12. V. Kh. Salikhov, “On reducibility and linear reducibility of linear differential equations,” Vestnik Moscow Univ. Ser. I Mat. Mekh., No. 3, 3–8 (1989).

    Google Scholar 

  13. A. I. Galochkin, “Estimates from below for linear forms in the values of certain hypergeometric functions,” Mat. Zametki,8, No. 1, 19–28 (1970).

    Google Scholar 

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Authors
  1. P. L. Ivankov
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Krasnogorsk. Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 34, No. 5, pp. 53–62, September–October, 1993.

Translated by V. N. Dyatlov

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Ivankov, P.L. On linear independence of the values of entire hypergeometric functions with irrational parameters. Sib Math J 34, 839–847 (1993). https://doi.org/10.1007/BF00971400

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  • DOI: https://doi.org/10.1007/BF00971400

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