CLASS NUMBER FORMULAS FOR CERTAIN BICYCLIC BIQUADRATIC NUMBER FIELDS AS FINITE SUMS INVOLVING JACOBI ELLIPTIC FUNCTIONS

摘要

We give formulas for the class numbers of bicyclic biquadratic number fields containing an imaginary quadratic field of class number one. The class number is expressed as a finite sum in terms of the basic Jacobi elliptic functions, playing a similar role as the trigonometric sine in Dirichlet classical class number formula.