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