Abstract :
We study the divisibility of the strict class numbers of the quadratic fields of discriminant 8p, −8p, and −4p by powers of 2 for p ≡ 1 mod 4 a prime number. Various criteria for divisibility by 8 are discussed, and an analogue of the relation 8h+8p ↔ 8h−8p and 8h−4p is given for divisibility by 16. We present numerical data related to the known and conjectured densities of primes p giving rise to specific 2-power divisibilities.
