Milovic, D;
(2018)
ON THE 8-RANK OF NARROW CLASS GROUPS OF Q(
√
−4pq),
Q(
√
−8pq), AND Q(
√
8pq).
International Journal of Number Theory
, 14
(8)
pp. 2165-2193.
10.1142/S1793042118501300.
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Abstract
Let d∈{−4,−8,8}. We study the 8-part of the narrow class group in thin families of quadratic number fields of the form Q(dpq−−−√), where p≡q≡1mod4 are prime numbers, and we prove new lower bounds for the proportion of narrow class groups in these families that have an element of order 8. In the course of our proof, we prove a general double-oscillation estimate for the quadratic residue symbol in quadratic number fields.
| Type: | Article |
|---|---|
| Title: | ON THE 8-RANK OF NARROW CLASS GROUPS OF Q( √ −4pq), Q( √ −8pq), AND Q( √ 8pq) |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1142/S1793042118501300 |
| Publisher version: | https://doi.org/10.1142/S1793042118501300 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10073324 |
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