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Relations in the Ideal Classes
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A(pn abelian extension abelian group adic algebraic number assume automorphism Bernoulli numbers Bernoulli polynomials Chapter class field theory class number coefficients computation concludes the proof congruence cyclotomic fields cyclotomic units denote determinant distribution relation factor group follows formal group formal multiplicative group Galois group Gauss sum group ring Hence homomorphism ideal class group integer isomorphism Iwasawa algebra Kummer Leopoldt logarithm Lubin-Tate group maximal abelian maximal ideal mod pn module non-trivial norm notation number field obvious p-adic positive integer power series power series associated prime power primitive projective limit proves the lemma proves the theorem quasi-isomorphism residue class root of unity satisfies shows Stickelberger ideal suffice to prove Suppose surjective symbol Teichmuller character Theorem 2.2 totally ramified trivial unique unramified Vandiver conjecture vector write zeta function Zp-extension