摘要
For F = Q(√εpq), ε∈ {±1,±2}, primes -p ≡ q ≡ 1 mod 4, we give the necessary and sufficient conditions for 8-ranks of narrow class groups of F equal to 1 or 2 such that we can calculate their densities. All results are stated in terms of congruence relations of p, q modulo 2^n, the quartic residue symbol (1/q)4 and binary quadratic forms such as q^h(-2p)/^4 = x^2 + 2py^2 where h(-2p) is the class number of Q(√-2p). The results are very useful for numerical computations.
For F = Q(√εpq), ε∈ {±1,±2}, primes -p ≡ q ≡ 1 mod 4, we give the necessary and sufficient conditions for 8-ranks of narrow class groups of F equal to 1 or 2 such that we can calculate their densities. All results are stated in terms of congruence relations of p, q modulo 2^n, the quartic residue symbol (1/q)4 and binary quadratic forms such as q^h(-2p)/^4 = x^2 + 2py^2 where h(-2p) is the class number of Q(√-2p). The results are very useful for numerical computations.
基金
Supported by National Natural Science Foundation of China (Grant Nos. 10771100, 10971250)