An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree. (10th October 2022)
- Record Type:
- Journal Article
- Title:
- An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree. (10th October 2022)
- Main Title:
- An improvement on Schmidt's bound on the number of number fields of bounded discriminant and small degree
- Authors:
- Bhargava, Manjul
Shankar, Arul
Wang, Xiaoheng - Abstract:
- Abstract: We prove an improvement on Schmidt's upper bound on the number of number fields of degree n and absolute discriminant less than X for $6\leq n\leq 94$ . We carry this out by improving and applying a uniform bound on the number of monic integer polynomials, having bounded height and discriminant divisible by a large square, that we proved in a previous work [7].
- Is Part Of:
- Forum of mathematics. Volume 10(2022)
- Journal:
- Forum of mathematics
- Issue:
- Volume 10(2022)
- Issue Display:
- Volume 10, Issue 2022 (2022)
- Year:
- 2022
- Volume:
- 10
- Issue:
- 2022
- Issue Sort Value:
- 2022-0010-2022-0000
- Page Start:
- Page End:
- Publication Date:
- 2022-10-10
- Subjects:
- 11R04 -- 11R09 -- 58C40 -- 53A07
Mathematics -- Periodicals
510 - Journal URLs:
- http://journals.cambridge.org/action/displayJournal?jid=FMS ↗
- DOI:
- 10.1017/fms.2022.71 ↗
- Languages:
- English
- ISSNs:
- 2050-5094
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD Digital store
- Ingest File:
- 24021.xml