View : 245 Download: 0
Congruences for odd class numbers of quadratic fields with odd discriminant
- Title
- Congruences for odd class numbers of quadratic fields with odd discriminant
- Authors
- Kim J.; Mizuno Y.
- Ewha Authors
- 김지구
- SCOPUS Author ID
- 김지구
- Issue Date
- 2023
- Journal Title
- Ramanujan Journal
- ISSN
- 1382-4090
- Citation
- Ramanujan Journal vol. 60, no. 4, pp. 939 - 963
- Keywords
- Class numbers; Hirzebruch sums; Quadratic fields
- Publisher
- Springer
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- For any distinct two primes p1≡ p2≡ 3 (mod4), let h(- p1) , h(- p2) and h(p1p2) be the class numbers of the quadratic fields Q(-p1), Q(-p2) and Q(p1p2), respectively. Let ωp1p2:=(1+p1p2)/2 and let Ψ(ωp1p2) be the Hirzebruch sum of ωp1p2. We show that h(-p1)h(-p2)≡h(p1p2)Ψ(ωp1p2)/n(mod8), where n= 6 (respectively, n= 2) if minp1 , p2 > 3 (respectively, otherwise). We also consider the real quadratic order with conductor 2 in Q(p1p2). © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- DOI
- 10.1007/s11139-022-00673-2
- Appears in Collections:
- 연구기관 > 수리과학연구소 > Journal papers
- Files in This Item:
There are no files associated with this item.
- Export
- RIS (EndNote)
- XLS (Excel)
- XML