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- W2008349074 abstract "Let α 1 , …, α n be n ≥ 2 algebraic numbers such that log α 1 ,…, log α n and 2πi are linearly independent over the field of rational numbers Q . It is well known (see (6), Ch. 1) that the Thue–Siegel–Roth theorem implies that, for each positive number δ, there are only finitely many integers b 1 ,…, b n satisfying where H denotes the maximum of the absolute values of b 1 , …, b n . However, such an argument cannot provide an explicit upper bound for the solutions of (1), because of the non-effective nature of the theorem of Thue–Siegel–Roth. An effective proof that (1) has only a finite number of solutions was given by Gelfond (6) in the case n = 2, and by Baker(1) for arbitrary n . The work of both these authors is based on arguments from the theory of transcendental numbers. Baker's effective proof of (1) has important applications to other problems in number theory; in particular, it provides an algorithm for solving a wide class of diophantine equations in two variables (2)." @default.
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- W2008349074 date "1971-01-01" @default.
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- W2008349074 title "An application of the Thue–Siegel–Roth theorem to elliptic functions" @default.
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- W2008349074 doi "https://doi.org/10.1017/s030500410004651x" @default.
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