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From Baker to Mordell

In: International Symposium in Memory of Hua Loo Keng

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  • G. Wüstholz

    (ETH Zürich, ETH-Zentrum)

Abstract

The theory of linear forms in logarithms goes back to the seventh of Hilbert’s famous problems which Hilbert stated in 1900. This problem was solved in 1934 independently by Gelfond and Schneider. They proved namely that for algebraic α, β with α ≠ 0,1 and β irrational the number γ = αβ is transcendental. This statement is equivalent to the following qualitative statement. Suppose that α, β, γ are algebraic numbers and that log α, log γ are defined and not zero. Then if Λ =β log α − log γ satisfies Λ = 0 we have β ∈ ℚ.

Suggested Citation

  • G. Wüstholz, 1991. "From Baker to Mordell," Springer Books, in: Sheng Gong & Qi-Keng Lu & Yuan Wang & Lo Yang (ed.), International Symposium in Memory of Hua Loo Keng, pages 323-330, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-07981-2_19
    DOI: 10.1007/978-3-662-07981-2_19
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