Krasner's lemma is a result in the field of number theory, specifically dealing with linear forms in logarithms of algebraic numbers. It provides conditions under which a certain linear combination of logarithms can lead to a rational approximation or a specific form of representation. The lemma is often used in Diophantine approximation and transcendency theory.
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Let be complete, let be separable over , and let be algebraic over . If is closer to than any other -conjugate of , then