Baker's theorem

<p>In <a href="/facts/Transcendental_number_theory/tjyLHm5G">transcendental number theory</a>, a mathematical discipline, Baker's theorem gives a lower bound for the absolute value of <a href="/facts/Linear_combination/CVjL6kuN">linear combinations</a> of <a href="/facts/Logarithm/QeXaV97q">logarithms</a> of <a href="/facts/Algebraic_number/MkH1PzTK">algebraic numbers</a>. Nearly fifteen years earlier, <a href="/facts/Alexander_Gelfond/p0B6rsXt">Alexander Gelfond</a> had considered the problem with only integer coefficients to be of "extraordinarily great significance". The result, proved by <a href="/facts/Alan_Baker_(mathematician)/1BAzUSML">Alan Baker</a> (1966, 1967a, 1967b), subsumed many earlier results in transcendental number theory. Baker used this to prove the transcendence of many numbers, to derive effective bounds for the solutions of some <a href="/facts/Diophantine_equation/mYaHp7oX">Diophantine equations</a>, and to solve the <a href="/facts/Class_number_problem/bIrLDjde">class number problem</a> of finding all imaginary <a href="/facts/Quadratic_field/dUnSDN4e">quadratic fields</a> with <a href="/facts/Class_numbers_of_imaginary_quadratic_fields/o7oDA25G">class number</a> 1.
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Baker's theorem open-in-new

Baker's theorem