منابع مشابه
The Thue–Siegel–Roth Theorem
In this paper we will give a proof of the Thue-Siegel-Roth Theorem, which states that for any algebraic number α and any ǫ > 0 there exists only a finite number of pairs of coprime integers p, q such that ∣ α − p q ∣ ∣ < 1 q2+ǫ . We will follow the proof as it is presented Leveque’s book, [8, ch 4]. This proof also deals with the more general case when p q is allowed to be an algebraic number i...
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A proof of the transcendence of a real number ξ based on the Thue–Siegel–Roth–Schmidt method involves generally a sequence (αn)n≥1 of algebraic numbers of bounded degree or a sequence (xn)n≥1 of integer r-tuples. In the present paper, we show how such a proof can produce a transcendence measure for ξ, if one is able to quantify the growth of the heights of the algebraic numbers αn or of the poi...
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We give a quantitative version of Roth’s Theorem over an arbitrary number field, similar to that given by Bombieri and van der Poorten. Introduction. Let K/Q be a number field, with [K : Q] = d. Let MK be a complete set of inequivalent absolute values on K, normalized so that the absolute logarithmic height is given by h : K → [0,∞), h(x) = ∑
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Using Y.André's result on differential equations staisfied by E-functions, we derive an improved version of the Siegel-Shidlovskii theorem. It gives a complete characterisation of algebraic relations over the algebraic numbers between values of E-functions at any non-zero algebraic point.
متن کاملOn a Theorem of Aubry-thue
If a, b and m are relatively prime, then (1) can be solved by integers x and y such that \x\ ^ m, \y\ ^ m*. This is called, in general, the Theorem of Thue. See, for instance, the books of A. Scholz [7, p. 45], and O. Ore [5, p. 268]. If (b, m) = 1 and m is not a square, the results of Aubry and Thue are identical. If m is a square but b/m* is not an integer, then Aubry's result is better than ...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1959
ISSN: 0386-2194
DOI: 10.3792/pja/1195524207