Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 5
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Ito, Akiko 2015. Notes on the divisibility of the class numbers of imaginary quadratic fields $$\mathbb {Q}(\sqrt{3^{2e} - 4k^n})$$ Q ( 3 2 e - 4 k n ). Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, Vol. 85, Issue. 1, p. 1.


    MINHUI, ZHU and TINGTING, WANG 2012. THE DIVISIBILITY OF THE CLASS NUMBER OF THE IMAGINARY QUADRATIC FIELD. Glasgow Mathematical Journal, Vol. 54, Issue. 01, p. 149.


    ITO, AKIKO 2011. REMARKS ON THE DIVISIBILITY OF THE CLASS NUMBERS OF IMAGINARY QUADRATIC FIELDS. Glasgow Mathematical Journal, Vol. 53, Issue. 02, p. 379.


    KISHI, YASUHIRO 2010. ON THE IDEAL CLASS GROUP OF CERTAIN QUADRATIC FIELDS. Glasgow Mathematical Journal, Vol. 52, Issue. 03, p. 575.


    KISHI, YASUHIRO 2010. NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS – CORRIGENDUM. Glasgow Mathematical Journal, Vol. 52, Issue. 01, p. 207.


    ×

NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS

  • YASUHIRO KISHI (a1)
  • DOI: http://dx.doi.org/10.1017/S001708950800462X
  • Published online: 01 January 2009
Abstract
Abstract

We prove that the class number of the imaginary quadratic field is divisible by n for any positive integers k and n with 22k < 3n, by using Y. Bugeaud and T. N. Shorey's result on Diophantine equations.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      NOTE ON THE DIVISIBILITY OF THE CLASS NUMBER OF CERTAIN IMAGINARY QUADRATIC FIELDS
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.N. C. Ankeny and S. Chowla , On the divisibility of the class number of quadratic fields, Pacific J. Math. 5 (1955), 321324.

3.B. H. Gross and D. E. Rohrlich , Some results on the Mordell-Weil group of the Jacobian of the Fermat curve, Invent. Math. 44 (1978), 201224.

4.A. Herschfeld , The equation 2x − 3y = d, Bull. Amer. Math. Soc. 42 (1936), 231234.

5.H. Ichimura , Note on the class numbers of certain real quadratic fields, Abh. Math. Sem. Univ. Hamburg 73 (2003), 281288.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Keywords: