Abstract:
This paper investigates the arithmetic properties of the values of certain hypergeometric functions at points in an imaginary quadratic field I. Under certain conditions it is proved that these values are linearly independent over I. An effective lower bound is given for a linear form, which contains the maximum modulus of its coefficients. An estimate is also given which depends on the bounds within which each of the coefficients varies.
Bibliography: 11 titles.
\Bibitem{Sor85}
\by V.~N.~Sorokin
\paper On~the irrationality of the values of hypergeometric functions
\jour Math. USSR-Sb.
\yr 1986
\vol 55
\issue 1
\pages 243--257
\mathnet{http://mi.mathnet.ru/eng/sm1968}
\crossref{https://doi.org/10.1070/SM1986v055n01ABEH003002}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=792441}
\zmath{https://zbmath.org/?q=an:0594.10025|0575.10029}
Linking options:
https://www.mathnet.ru/eng/sm1968
https://doi.org/10.1070/SM1986v055n01ABEH003002
https://www.mathnet.ru/eng/sm/v169/i2/p245
This publication is cited in the following 10 articles:
Vaananen K., “On a Result of Fel'Dman on Linear Forms in the Values of Some E-Functions”, Ramanujan J., 48:1 (2019), 33–46
Merila V., “A Nonvanishing Lemma for Certain Pade Approximations of the Second Kind”, Int. J. Number Theory, 7:8 (2011), 1977–1997
Merila V., “On the Linear Independence of the Values of Gauss Hypergeometric Function”, Acta Arith., 144:4 (2010), 349–371
Yao Chen Zhu, “Discrepancy of Certain Kronecker Sequences Concerning Transcendental Numbers”, Acta. Math. Sin.-English Ser., 23:10 (2007), 1897–1902
T. G. Hessami Pilehrood, Kh. Hessami Pilehrood, “Lower bounds for linear forms in values of polylogarithms”, Math. Notes, 77:4 (2005), 573–579
Vaananen, K, “Baker-type estimates for linear forms in the values of q-series”, Canadian Mathematical Bulletin-Bulletin Canadien de Mathematiques, 48:1 (2005), 147
Marc HUTTNER, “ON LINEAR INDEPENDENCE MEASURES OF SOME ABELIAN INTEGRALS”, Kyushu J. Math., 57:1 (2003), 129
T. G. Hessami Pilehrood, “Lower bounds for linear forms in values of certain hypergeometric functions”, Math. Notes, 67:3 (2000), 372–381
M. Prévost, “Diophantine approximations using Padé approximations”, Journal of Computational and Applied Mathematics, 122:1-2 (2000), 231
Aptekarev, AI, “Multiple orthogonal polynomials”, Journal of Computational and Applied Mathematics, 99:1–2 (1998), 423
Citation in format AMSBIB
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