Geodesic
On the Algebraic Properties of Solutions of Inhomogeneous Hypergeometric Equations
Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 658-672.

Voir la notice de l'article provenant de la source Math-Net.Ru

Generalized hypergeometric differential equations of arbitrary order are considered. Necessary and sufficient conditions for the algebraic independence of solutions of collections of such equations, as well as of their values at algebraic points, are obtained.
Keywords: hypergeometric differential equation, algebraic independence of solutions, algebraic point
Mots-clés : Galois group. 
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V. A. Gorelov. On the Algebraic Properties of Solutions of Inhomogeneous Hypergeometric Equations. Matematičeskie zametki, Tome 99 (2016) no. 5, pp. 658-672. http://geodesic.mathdoc.fr/item/MZM_2016_99_5_a2/

[1] V. A. Gorelov, “Ob algebraicheskoi nezavisimosti znachenii obobschennykh gipergeometricheskikh funktsii”, Matem. zametki, 94:1 (2013), 94–108 | DOI | MR | Zbl

[2] C. L. Siegel, “Über einige Anwendungen Diophantischer Approximationen”, Abh. Preuss. Acad. Wiss., Phys.-Math. Kl., 1929, no. 1, 1–70 | Zbl

[3] A. B. Shidlovskii, Transtsendentnye chisla, Nauka, M., 1987 | MR | Zbl

[4] F. Beukers, W. D. Brownawell, G. Heckman, “Siegel normality”, Ann. of Math. (2), 127:2 (1988), 279–308 | DOI | MR | Zbl

[5] F. Beukers, “Some new results on algebraic independence of E-functions”, New Advances in Transcendence Theory, Cambridge Univ. Press, Cambridge, 1988, 56–67 | MR | Zbl

[6] V. Kh. Salikhov, “Kriterii algebraicheskoi nezavisimosti znachenii odnogo klassa gipergeometricheskikh $E$-funktsii”, Matem. sb., 181:2 (1990), 189–211 | MR | Zbl

[7] E. R. Kolchin, “Algebraic groups and algebraic dependence”, Amer. J. Math., 90:4 (1968), 1151–1164 | DOI | MR | Zbl

[8] N. M. Katz, Exponential Sums and Differential Equations, Ann. of Math. Stud., 124, Princeton Univ. Press, Princeton, NJ, 1990 | MR | Zbl

[9] M. A. Cherepnev, “Ob algebraicheskoi nezavisimosti nekotorykh podklassov gipergeometricheskikh funktsii”, Matem. zametki, 55:1 (1994), 117–129 | MR | Zbl

[10] V. Kh. Salikhov, “Kriterii algebraicheskoi nezavisimosti znachenii gipergeometricheskikh $E$-funktsii (chetnyi sluchai)”, Matem. zametki, 64:2 (1998), 273–284 | DOI | MR | Zbl

[11] Yu. V. Nesterenko, “Ob algebraicheskoi nezavisimosti znachenii $E$-funktsii, udovletvoryayuschikh lineinym neodnorodnym differentsialnym uravneniyam”, Matem. zametki, 5:5 (1969), 587–598 | MR | Zbl

[12] D. Bertrand, “Un analogue différentiel de la théorie de Kummer”, Approximations Diophantiennes et Nombres Transcendants (Luminy, 1990), de Gruyter, Berlin, 1992, 39–49 | MR | Zbl

[13] M. A. Cherepnev, “Ob algebraicheskoi nezavisimosti znachenii gipergeometricheskikh $E$-funktsii”, Matem. zametki, 57:6 (1995), 896–912 | MR | Zbl

[14] Dzh. Sansone, Obyknovennye differentsialnye uravneniya, T. 1, IL, M., 1953 | MR | Zbl

[15] A. Ostrowski, “Sur les relations algébriques entre les intégrales indéfinies”, Acta Math., 78 (1946), 315–318 | DOI | MR | Zbl

[16] V. Kh. Salikhov, “Neprivodimost gipergeometricheskikh uravnenii i algebraicheskaya nezavisimost znachenii $E$-funktsii”, Acta Arith., 53:5 (1990), 453–471 | MR | Zbl