Milovic, D;
(2017)
The Infinitude of Q(√
−p) With Class Number
Divisible by 16.
Acta Arithmetica
, 178
pp. 201-233.
10.4064/aa8147-2-2017.
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Abstract
Abstract. The density of primes p such that the class number h of Q( √ −p) is divisible by 2k is conjectured to be 2−k for all positive integers k. The conjecture is true for 1 ≤ k ≤ 3 but still open for k ≥ 4. For primes p of the form p = a 2 + c 4 with c even, we describe the 8-Hilbert class field of Q( √ −p) in terms of a and c. We then adapt a theorem of Friedlander and Iwaniec to show that there are infinitely many primes p for which h is divisible by 16, and also infinitely many primes p for which h is divisible by 8 but not by 16.
| Type: | Article |
|---|---|
| Title: | The Infinitude of Q(√ −p) With Class Number Divisible by 16 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4064/aa8147-2-2017 |
| Publisher version: | https://doi.org/10.4064/aa8147-2-2017 |
| 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. |
| Keywords: | math.NT, math.NT |
| 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.ucl.ac.uk/id/eprint/10048219 |
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