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
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 Σ
p -1n=1nk(
n/
p).
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