Keywords and phrases: class number, real quadratic field.
Received: April 5, 2022; Accepted: May 19, 2022; Published: May 25, 2022
How to cite this article: Anly Li, On class number one for the real quadratic field , JP Journal of Algebra, Number Theory and Applications 55 (2022), 79-84. http://dx.doi.org/10.17654/0972555522021
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
[1] Azizul Hoque and Srinivas Kotyda, Class number one problem for the real quadratic fields Arch. Math. (Basel) 116 (2021), 33-36. [2] Keith Conrad, The conductor ideal of an order. [3] C. Latimer and C. C. MacDuffee, A correspondence between classes of ideals and classes of matrices, Ann. of Math. 34 (1933), 313-316. [4] S. Louboutin, Continued fractions and real quadratic fields, J. Number Theory 30(2) (1988), 167-176. [5] S. Louboutin, Prime producing quadratic polynomials and class-numbers of real quadratic fields, Canad. J. Math. 42(2) (1990), 315-341. [6] M. Newman, Integral Matrices, Academic Press, New York, 1972. [7] O. Taussky, On a theorem of Latimer and MacDuffee, Canad. J. Math. 1 (1949), 300-302. [8] D. I. Wallace, Conjugacy classes of hyperbolic matrices in and ideal classes in an order, Trans. Amer. Math. Soc. 283 (1984), 177-184.
|