## A class number formula for certain quartic fields |

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2bCD abelian extension Albert Appealing Berndt Carleton University character mod class number formula class number h(K completes the proof complex conjugate compute h(K cyclic field defined Denoting the fundamental Department of Mathematics Dirichlet's discriminant d(K Edgar and Peterson evaluate the quantities explicit formula extension of Q field with G(k/q formula 6.2 formula for h(K fundamental unit gives Hence Hudson and Kenneth identity of Cauchy integers J L(l Mathematics and Statistics mod 2b mod q modulo non-principal characters notation obtain occur Peterson 11 possesses a unique prime proof of Theorem qU)C Quartic Fields Richard regulator R(K result of Edgar Richard H right-hand side root of unity second possibility small values South Carolina subgroup sums Table of Class trivial unique quadratic subfield unit of Q(/q University of South values given values of q Williams Xl(n