If chosen logarithms of algebraic numbers are linearly independent over , then they, together with one, are linearly independent over . More generally a nonzero homogeneous linear combination with algebraic coefficients is transcendental. Quantitative lower bounds for integer coefficients are a separate, effective aspect of logarithmic-form theory.
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Baker's theorem pertains to the field of complex analysis, specifically dealing with functions that can be expressed through power series. More formally, it relates to the growth of meromorphic functions, which are functions that are holomorphic (complex differentiable) everywhere except for a set of isolated poles.