Linear Forms in the Logarithms of Algebraic Numbers with Small Coefficients I
Abstract
Ifav α1, α2, β1 are rational numbers satisfying (i) α1 > 0, α2 > 0 are multiplicatively independent (ii) the size of α1, α2, β1, respectively, do not exceed S1, S1 and (log S1)100 (100 is quite unimportant), then | β1 log α1 - log α2| > C(∈) exp ( - (log S1)2+z) (1) where ∈ > 0 is an arbitrary fixed constant and C(∈) is an effectively computable positive constant depending only on ∈.Downloads
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Copyright (c) 1974 T. N. Shorey
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References
A. BAKER, Linear forms in the logarithms of algebraic numbers I, Mathematika, 13(1966), pp. 204-16.
A. BAKER, Linear forms in the logarithms of algebraic numbers II, Mathematika, 14 (1967), pp. 102-07.
P. ERDOS, On consecutive Integers, Nieuw, Arch. Voor. Wiskunde, 3 (1951), pp. 268-273.
K. RAMACHANDRA, A note on numbers with a large prime factor III, Acta Arithmetica, 19 (1971).
K. RAMACHANDRA, Lectures on Transcendental Numbers. The Ramanujan Institute, Madras (1969).
K. RAMACHANDRA, Contributions to the Theory of Transcendental Numbers II, Acta Arithmetica, Vol. 14 (1968).
T.N. SHOREY, On a theorem of Ramachandra Acta Airth. 20 (1972), 215-221.
R. TuDEMAN, On the maximal distance of numbers with a large prime factor Jour. Lond. Math. Soc. 5 (1972), 313-320.
R. TIJDEMAN, An auxliary Result in the theory of transcendental Numbers Jour. Num. Theory. 5 (1973), 80-94.