A DEFORMATION OF THE CLASS NUMBER FORMULA OF REAL QUADRATIC FIELDS

Abstract

For an odd square-free integer n, there exists a polynomial L(n)(x) such that L(n)(x) = square-root phi(n)(sx2) exp (- s' square-root ng(n)(x)) [GRAPHICS] Using the fact that the value of g(n)(1) is related to the class number h(D) of the real quadratic field Q(square-root n) with discriminant D, we deduce a deformation of the class number formula.