JOURNAL BROWSE
Search
Advanced SearchSearch Tips
8-RANKS OF CLASS GROUPS OF IMAGINARY QUADRATIC NUMBER FIELDS AND THEIR DENSITIES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
8-RANKS OF CLASS GROUPS OF IMAGINARY QUADRATIC NUMBER FIELDS AND THEIR DENSITIES
Jung, Hwan-Yup; Yue, Qin;
  PDF(new window)
 Abstract
For imaginary quadratic number fields F
 Keywords
class group;unramified extension;quartic residue;density;
 Language
English
 Cited by
1.
Congruent elliptic curves with non-trivial Shafarevich-Tate groups, Science China Mathematics, 2016, 59, 11, 2145  crossref(new windwow)
 References
1.
P. Barrucand and H. Cohn, Note on primes of type $x^{2}+32y^{2}$, class number, and residuacity, J. Reine Angew. Math. 238 (1969), 67-70.

2.
P. E. Conner and J. Hurrelbrink, Class Number Parity, Ser. Pure Math. 8, Would Sci., Singapore 1988.

3.
P. E. Conner and J. Hurrelbrink, On the 4-rank of the tame kernel $K_{2}$(O) in positive definite terms, J. Number Theory 88 (2001), no. 2, 263-282. crossref(new window)

4.
F. Gerth III, Counting certain number fields with prescibed l-class numbers, J. Reine Angew. Math. 337 (1982), 195-207.

5.
F. Gerth III, The 4-class ranks of quadratic fields, Invent. Math. 77 (1984), no. 3, 489-515. crossref(new window)

6.
F. Gerth III and S. W. Graham, Application of a character sum estimate to a 2-class number density, J. Number Theory 19 (1984), no. 2, 239-247. crossref(new window)

7.
G. Hardy and E. Wright, An Introduction to the Theory of Numbers, Fifth edition, London, 1979.

8.
E. Hecke, Lecture on the Theory of Algebraic Numbers, GTM 77, Springer-Verlag, 1981.

9.
J. Hurrelbrink and Q. Yue, On ideal class groups and units in terms of the quadratic form $x^{2}+32y^{2}$, Chinese Ann. Math. Ser. B 26 (2005), no. 2, 239-252. crossref(new window)

10.
K. Ireland and M. Rosen, A Classical Introduction to Modern Number Theory, GTM 84, Springer-Verlag, 1972.

11.
J. Neukirch, Class Field Theory, Springer, Berlin, 1986.

12.
P. Stevenhagen, Divisibity by 2-powers of certain quadratic class numbers, J. Number Theory 43 (1993), no. 1, 1-19. crossref(new window)

13.
X. Wu and Q. Yue, 8-ranks of class groups of some imaginary quadratic number fields, Acta Math. Sin. (Engl. Ser.) 23 (2007), no. 11, 2061-2068. crossref(new window)

14.
Q. Yue, On tame kernel and class group in terms of quadratic forms, J. Number Theory 96 (2002), no. 2, 373-387. crossref(new window)

15.
Q. Yue, 8-ranks of class groups of quadratic number fields and their densities, Acta Matematica Sinica (Eng. Ser.), to apppear.

16.
Q. Yue and J. Yu, The densities of 4-ranks of tame kernels for quadratic fields, J. Reine Angew. Math. 567 (2004), 151-173.