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.
“…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].…”
Section: A Characterization Using Hilbert Symbolssupporting
“…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].…”
Section: A Characterization Using Hilbert Symbolssupporting
“…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.…”
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.