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We obtain a formula for the discriminant D κ/Q of an algebraic number field κ in terms of a ratio of the first two coefficients of the Taylor series of ζ κ at 1/2. Let κ be a number field of degree n = r 1 + 2r 2 , where r 1 , r 2 are the number of real, complex places respectively. The Dedekind ζ-function of the number field κ is defined by the series where a varies over the non-zero integral ideals of κ and N (a) denotes the absolute norm of a. Denote by D κ/Q the discriminant of κ. Thedoi:10.1090/s0002-9939-2010-10546-4 fatcat:jasu7xuxxzftbkuk2xhepeuhny