Leopoldt’s conjecture

Let $K$ be a number field, and let $p$ be a rational prime. Then $R_{p}(K)\eq 0$ , where $R_{p}(K)$ denotes the $p$ -adic regulator (http://planetmath.org/PAdicRegulator) of $K$ .

Though unproven for number fields in general, it is known to be true for abelian extensions of $\\mathbb{Q}$ , and for certain non-abelian 2-extensions of imaginary quadratic extensions of $\\mathbb{Q}$ .

References

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

单词	LeopoldtsConjecture
释义	Leopoldt’s conjecture Let $K$ be a number field, and let $p$ be a rational prime. Then $R_{p}(K)\eq 0$ , where $R_{p}(K)$ denotes the $p$ -adic regulator (http://planetmath.org/PAdicRegulator) of $K$ . Though unproven for number fields in general, it is known to be true for abelian extensions of $\\mathbb{Q}$ , and for certain non-abelian 2-extensions of imaginary quadratic extensions of $\\mathbb{Q}$ . References 1 L. C. Washington, Introduction to Cyclotomic Fields,Springer-Verlag, New York.
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