ON CLASS NUMBERS OF QUADRATIC FIELDS WITH PRIME DISCRIMINANT AND CHARACTER SUMS

We investigate the values of Dirichlet L-functions L(s, χp) at s = 1 as p runs through the primes in an arithmetic progression, where χp denotes the character given by Legendre' s symbol (•/p). We show that the numbers hQ(√-p)/√p exist densely in the positive real numbers, where hQ(√-p) is the class number of the quadratic field Q(√-p).We also give a quantitative result for the problem of Ayoub, Chowla and Walum [ACW] about the character sum Σp -1n=1nk(n/p).