Top

Published in:

2024 | OriginalPaper | Chapter

Parameterized Families of Quadratic Fields with n-Rank at Least 2

Authors : Azizul Hoque, Kotyada Srinivas

Published in: Class Groups of Number Fields and Related Topics

Publisher: Springer Nature Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We construct parameterized families of imaginary (resp. real) quadratic fields whose class groups have n-rank at least 2.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Note on the Rank of 2-Class Group of

next chapter On the Divisibilities , , and

Byeon, D.: Imaginary quadratic fields with noncyclic ideal class groups. Ramanujan J. 11(2), 159–163 (2006)MathSciNetCrossRef

Chakraborty, K., Ram Murty, M.: On the number of real quadratic fields with class number divisible by 3. Proc. Am. Math. Soc. 131(1), 41–44 (2003)

Chakraborty, K., Hoque, A., Kishi, Y., Pandey, P.P.: Divisibility of the class numbers of imaginary quadratic fields. J. Number Theory 185, 339–348 (2018)MathSciNetCrossRef

Chakraborty, K., Hoque, A.: Exponents of class groups of certain imaginary quadratic fields. Czechoslovak Math. J. 70(4), 1167–1178 (2020)MathSciNetCrossRef

Chakraborty, K., Hoque, A.: Lehmer sequence approach to the divisibility of class numbers of imaginary quadratic fields. Ramanujan J. 60(4), 913–923 (2023)MathSciNetCrossRef

Cohen, H., Lenstra Jr., H.W.: Heuristics on class groups of number fields. In: Number Theory, Noordwijkerhout, 1983. Lecture Notes in Mathematics, vol. 1068, pp. 33–62. Springer, Berlin (1984)

Craig, M.: A type of class group for imaginary quadratic fields. Acta Arith. 22, 449–459 (1973)MathSciNetCrossRef

Craig, M.: A construction for irregular discriminants. Osaka J. Math. 14, 365–402 (1977)MathSciNet

Erickson, C., Kaplan, N., Mendoza, N., Pacelli, A.M., Shayler, T.: Parameterized families of quadratic number fields with \(3\)-rank at least \(2\). Acta Arith. 130(2), 141–147 (2007)MathSciNetCrossRef

10.

Hoque, A.: On the exponents of class groups of some families of imaginary quadratic fields. Mediterr. J. Math. 18(4), Paper No. 153, 13 (2021)

11.

Hoque, A.: On a conjecture of Iizuka. J. Number Theory 238, 464–473 (2022)MathSciNetCrossRef

12.

Llorente, P., Nart, E.: Effective determination of the decomposition of rational primes in a cubic field. Proc. Am. Math. Soc. 87, 579–585 (1983)MathSciNetCrossRef

13.

Llorente, P., Quer, J.: On the \(3\)-Syllow group of the class group of quadratic fields. Math. Comp. 50, 321–333 (1988)MathSciNetCrossRef

14.

Luca, F., Pacelli, A.M.: Class groups of quadratic fields of \(3\)-rank at least \(2\): effective bounds. J. Number Theory 128(4), 796–804 (2008)MathSciNetCrossRef

15.

Kishi, Y., Komatsu, T.: Imaginary quadratic fields whose ideal class groups have \(3\)-rank at least three. J. Number Theory 170, 46–54 (2017)MathSciNetCrossRef

16.

Mestre, J.F.: Courbes elliptiques et groups de classes d’idéaux de certains corps quadratiques. In: Seminar on Number Theory, 1979/1980, Exp. No. 15, pp. 18. University Bordeaux I, Talence (1980)

17.

Mestre, J.F.: Groupes de classes d’idéaux non cyclique de corps de nombre. In: Seminar on Number Theory, Paris 1981/1982, 189–200, Progress in Mathematics, vol. 38. Birkhäuser, Boston, MA (1983)

18.

Nagell, T.: Über die Klassenzahl imaginär quadratischer, Zählkörper. Abh. Math. Semin. Univ. Hambg. 1, 140–150 (1922)CrossRef

19.

Quer, J.: Corps quadratiques de 3-rang 6 et courbes elliptiques de rang 12, C. R. Acad. Sci. Paris Sér. I Math. 305, 215–218 (1987)

20.

Soundararajan, K.: Divisibility of class numbers of imaginary quadratic fields. J. Lond. Math. Soc. 61, 681–690 (2000)MathSciNetCrossRef

21.

Weinberger, P.J.: Real quadratic fields with class numbers divisible by \(n\). J. Number Theory 5, 237–241 (1973)MathSciNetCrossRef

22.

Yamamoto, Y.: On unramified Galois extensions of quadratic number fields. Osaka J. Math. 7, 57–76 (1970)MathSciNet

23.

Yu, G.: A note on the divisibility of class numbers of real quadratic fields. J. Number Theory 97, 35–44 (2002)MathSciNetCrossRef

24.

Yu, G.: Imaginary quadratic fields with class groups of \(3\)-rank at least \(2\). Manuscripta Math. 163(3–4), 569–574 (2020)MathSciNetCrossRef

Title: Parameterized Families of Quadratic Fields with n-Rank at Least 2
Authors: Azizul Hoque
Kotyada Srinivas
Publisher: Springer Nature Singapore
Book: Class Groups of Number Fields and Related Topics
Print ISBN: 978-981-9769-10-0

Electronic ISBN: 978-981-9769-11-7

Copyright Year: 2024
DOI: https://doi.org/10.1007/978-981-97-6911-7_9

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"