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单词 LeopoldtsConjecture
释义

Leopoldt’s conjecture


Let K be a number fieldMathworldPlanetmath, and let p be a rational prime. Then Rp(K)0, where Rp(K) denotes the p-adic regulatorMathworldPlanetmath (http://planetmath.org/PAdicRegulator) of K.

Though unproven for number fields in general, it is known to be true for abelian extensionsMathworldPlanetmathPlanetmath of , and for certain non-abelianMathworldPlanetmathPlanetmath 2-extensions of imaginary quadratic extensions of .

References

  • 1 L. C. Washington, Introduction to Cyclotomic FieldsMathworldPlanetmath,Springer-Verlag, New York.
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