Character sums and the series L(1,X) with applications to real quadratic fields

In this article, let k = 0 or 1 (mod 4) be a fundamental discriminant, and let X(n) be the real even primitive character modulo k. The series L(1,X)=(sigma) x(n)/ (n) can be divided into groups of k consecutive terms. Let v be any nonnegative integer, j an integer, 0 < j max{l, (radical k/ |M|) if M = (sigma(m=1) x(m)+1/2x(j) (not equal)0 and |M|>3/2 In section 3, we will derive algorithm and formula for calculating the class number of a real quadratic field. In section 4, we will attempt to make a connection between two conjectures on real quadratic fields and the sign of T(0,20,x).