A REMARK OF SOME IMAGINARY QUADRATIC FIELDS WITH ODD CLASS NUMBERS

• Journal title : Honam Mathematical Journal
• Volume 36, Issue 1,  2014, pp.147-155
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2014.36.1.147
Title & Authors
A REMARK OF SOME IMAGINARY QUADRATIC FIELDS WITH ODD CLASS NUMBERS
Kim, Hyun; Lee, Keumyeon; Cheong, Cheoljo; Park, Hwasin;

Abstract
Let D be a square-free positive integer and let $\small{K_D=\mathbb{Q}(\sqrt{-D})}$ be the imaginary quadratic field. And let $\small{h_D}$ be the class number of the number field $\small{K_D}$. In this paper, we show the following: If D=l or 4l, where l is a prime number with $\small{l{\equiv}3}$ (mod 4), then $\small{h_D}$ is odd.
Keywords
class number;
Language
English
Cited by
References
1.
Z. I. Borevich and I. R. Shafarevich, Number Theory, New York, 1966.

2.
H. Cohn, Advanced number theory, New York, Dover, 1980.

3.
L. E. Dickson, Introduction to the Theory of Numbers, New York, Dover, 1957.

4.
J. Oesterla, Nombres de classes des corps quadratiques imaginaries, Asttrique (1985), 121-122, 309-323.

5.
P. Ribenboim, Algebraic Numbers, John Wiley and Sons, Inc, 1972.