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Analytic subgroup theorem
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<p>In mathematics, the analytic subgroup theorem is a significant result in modern <a href="/facts/Transcendental_number_theory/tjyLHm5G">transcendental number theory</a>. It may be seen as a generalisation of <a href="/facts/Baker%2527s_theorem/GXcd8RbV">Baker's theorem</a> on linear forms in logarithms. <a href="/facts/Gisbert_W%25C3%25BCstholz/FSPgk0lN">Gisbert Wüstholz</a> proved it in the 1980s. It marked a breakthrough in the theory of transcendental numbers. Many longstanding open problems can be deduced as direct consequences. </p>