On Class Numbers of Real Quadratic Fields with Certain Fundamental Discriminants

Authors

  • Ayten Pekin Istanbul University, faculty of sciences, department of mathematics
  • Aydin Carus

Keywords:

quadratic number field, class number

Abstract

Let $N$ denote the sets of positive integers and $D \inN$ be square free,and let χD ,  $h = h(D)denotethenon−trivialDirichletcharacter,theclassnumberoftherealquadraticeldK = Q\sqrt(D),respectivelyÂONO,provedthetheoremin[8]byapplyingSturm′sTheoremonthecongruenceofmodularformtoCohen′shalfintegralweightmodularforms.Later,DonghoByeonprovedatheoremandcorollaryin[1]byreningOno′methods.ÂInthispaper,wewillgiveatheoremforcertainrealquadraticfields.byconsideringÂabovementionedstudies.Todothis,weshallobtainanupperbounddifferentfromcurrentboundsforL(1; \chi_D)$ and use Dirichlet's class number formula.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Downloads

Additional Files

Published

2015-10-28

Issue

Vol. 8 No. 4: (October 2015)

Section

Number Theory

License

Upon acceptance of an article by the European Journal of Pure and Applied Mathematics, the author(s) retain the copyright to the article. However, by submitting your work, you agree that the article will be published under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). This license allows others to copy, distribute, and adapt your work, provided proper attribution is given to the original author(s) and source. However, the work cannot be used for commercial purposes.

By agreeing to this statement, you acknowledge that:

  • You retain full copyright over your work.
  • The European Journal of Pure and Applied Mathematics will publish your work under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
  • This license allows others to use and share your work for non-commercial purposes, provided they give appropriate credit to the original author(s) and source.

How to Cite

On Class Numbers of Real Quadratic Fields with Certain Fundamental Discriminants. (2015). European Journal of Pure and Applied Mathematics, 8(4), 526-529. https://www.ejpam.com/index.php/ejpam/article/view/2420