Theorem of Baker

The theorem of Baker , due to A. Baker in a series of articles entitled Linear forms in the logarithms off algebraic numbers appeared in 1966 and 1967 in the Mathematika review, is a result of transcendence on the Logarithme S of algebraic numbers, which generalizes the Théorème of Gelfond-Schneider. This theorem was adapted to the case of the p-adic numbers by Brumer, always in 1966; the Théorème of Brumer makes it possible to in the case of show the Conjecture of Leopoldt an abelian body of numbers, according to an article of Ax published in 1965.

Theorem Is $a\_1,\dots ,\; a\_n$ of the complex numbers whose Exponentielle S are algebraic on the body of the Rationnel S. If $a\_1,\dots ,\; a\_n$ are linearly independent on the body of rational then the $1,\; a\_1,\dots ,\; a\_n$ are linearly independent on the algebraic fence of the body of the rational ones.

Example: one from of deduced the transcendence from numbers such as log (2) + log (3) + log (5).

Category: Analysis complexes

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