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- W1967814134 abstract "Given a sequence of linear forms in m ≥ 2 complex or p -adic numbers α 1 , …,α m ∈ K v with appropriate growth conditions, Nesterenko proved a lower bound for the dimension d of the vector space Kα 1 + ··· + K α m over K, when K = Q and v is the infinite place. We shall generalize Nesterenko's dimension estimate over number fields K with appropriate places v , if the lower bound condition for | R n | is replaced by the determinant condition. For the q -series approximations also a linear independence measure is given for the d linearly independent numbers. As an application we prove that the initial values F ( t ), F ( qt ), …, F ( q m −1 t ) of the linear homogeneous q -functional equation where N = N ( q, t ), P i = P i ( q, t ) ∈ K[ q, t ] ( i = 1, …, m ), generate a vector space of dimension d ≥ 2 over K under some conditions for the coefficient polynomials, the solution F ( t ) and t, q ∈ K*." @default.
- W1967814134 created "2016-06-24" @default.
- W1967814134 creator A5028568585 @default.
- W1967814134 date "2002-06-01" @default.
- W1967814134 modified "2023-09-27" @default.
- W1967814134 title "On Diophantine approximations of the solutions of <i>q</i>-functional equations" @default.
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- W1967814134 doi "https://doi.org/10.1017/s0308210500001827" @default.
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