Abstract
Dirichlet (J Reine Angew Math 24, 1842) announced a generalization of his class number formula for real quadratic fields to biquadratic fields containing \({\mathbb{Q}(i)}\), by replacing the circular trigonometric functions with certain elliptic trigonometric functions. Subsequently, Nazimow (Ann Sci Ecole Norm Sup (3) 5:147–176, 1888) published the corresponding formula. Here we analyze the Dirichlet–Nazimow formula and update its proof in the context of Class Field Theory.
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More From: Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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