On the 4-rank of class groups of quadratic number fields

Abstract

We show that for 100% of the odd, squarefree integers n > 0 the 4-rank of Cl(Q(i, √ n)) is equal to ω 3 (n) − 1, where ω 3 is the number of prime divisors of n that are 3 modulo 4.

Ternary quadratic forms with rational zeros

“…The problem thus reduces to the estimation of sums over Hilbert symbols and thereby to sums over Jacobi symbols. Similar sums also occur in the very recent work of Fouvry and Klüners [3].…”

The 8-rank of tame kernels of quadratic number fields

“…It is just what happened in [4]. If you compare Theorem 3 of [4] with the formulae (1.5) and (1.6) of [5], you can see the analogous accordance.…”

On the 4-rank of tame kernels of quadratic number fields

“…It is just what happened in [4]. If you compare Theorem 3 of [4] with the formulae (1.5) and (1.6) of [5], you can see the analogous accordance. I would like to mention that Theorems 3.1 and 3.2 of [17] gave a strong support for Theorem 1.3 above.…”