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Leopoldt's conjecture
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<p>In <a href="/facts/Algebraic_number_theory/LPzDT5CA">algebraic number theory</a>, Leopoldt's conjecture, introduced by <a href="/facts/Heinrich-Wolfgang_Leopoldt/xSbeLDXc">H.-W. Leopoldt</a> (1962, 1975), states that the p-adic regulator of a <a href="/facts/Algebraic_number_field/e0K0TXSh">number field</a> does not vanish. The p-adic regulator is an analogue of the usual <a href="/facts/Regulator_(mathematics)/IQDk3QAR">regulator</a> defined using p-adic logarithms instead of the usual logarithms, introduced by <a href="/facts/Heinrich-Wolfgang_Leopoldt/xSbeLDXc">H.-W. Leopoldt</a> (1962). </p>