Author:
Kostadinka LapkovaDepartment of Mathematics and its Applications, Central European University, Nádor u. 9, 1051 Budapest, Hungary

Search for other papers by Kostadinka Lapkova in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

We prove the existence of infinitely many imaginary quadratic fields whose discriminant has exactly three distinct prime factors and whose class group has an element of a fixed large order. The main tool we use is solving an additive problem via the circle method.

  • [1] Balog, A. and Ono, K., Elements of class groups and Shafarevich–Tate groups of elliptic curves, Duke Math. J., (2003), 3563.

  • [2] Brüdern, J. Kawada, K. Wooley, T. D. 2000 Additive representation in thin sequences, II: The binary Goldbach problem Mathematica 47 117125.

    • Search Google Scholar
    • Export Citation
  • [3] Byeon, D. Lee, Sh. 2008 Divisibility of class numbers of imaginary quadratic fields whose discriminant has only two prime factors Proc. Japan Acad. Ser. A 84 810 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [4] Davenport, H. 2000 Multiplicative Number Theory 3 Springer.

  • [5] Hardy, G. H. Wright, E. M. 1979 An Introduction to the Theory of Numbers Oxford Univ. Press New York.

  • [6] Lapkova, K., Class number one problem for real quadratic fields of certain type, to appear in Acta Arith..

  • [7] Soundararajan, K. 2000 Divisibility of class numbers of imaginary quadratic fields J. London Math. Soc. (2) 61 681690 .

  • [8] Vaughan, R. C. 1981 The Hardy–Littlewood Method Cambridge Tracts in Math. 80 Cambridge Univ. Press Cambridge.

  • Collapse
  • Expand

To see the editorial board, please visit the website of Springer Nature.

Manuscript Submission: HERE

For subscription options, please visit the website of Springer Nature.

Acta Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1950
Volumes
per Year
3
Issues
per Year
6
Founder Magyar Tudományos Akadémia  
Founder's
Address
H-1051 Budapest, Hungary, Széchenyi István tér 9.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0236-5294 (Print)
ISSN 1588-2632 (Online)

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Aug 2022 6 1 0
Sep 2022 4 0 0
Oct 2022 1 1 0
Nov 2022 6 0 0
Dec 2022 2 0 0
Jan 2023 4 0 0
Feb 2023 0 0 0