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

Abstract

We investigate the values of Dirichlet L-functions L(s, χ_p) at s = 1 as p runs through the primes in an arithmetic progression, where χ_p denotes the character given by Legendre' s symbol (•/p). We show that the numbers h_Q(√-p)/√p exist densely in the positive real numbers, where h_Q(√-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 Σ^{p -1}_n=1n^k(n/p).