HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS

Title & Authors
HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS
Jung, Hwanyup;

Abstract
In this paper we study the infiniteness of Hilbert 2-class field towers of real quadratic function fields over $\small{\mathbb{F}_q(T)}$, where q is a power of an odd prime number.
Keywords
Hilbert 2-class field tower;real quadratic function field;
Language
English
Cited by
References
1.
S. Bae, S. Hu, and H. Jung, The generalized R'edei matrix for function fields, Finite Fields Appl. 18 (2012), no 4, 760-780.

2.
F. Gerth, Quadratic fields with infinite Hilbert 2-class field towers, Acta Arith. 106 (2003), no. 2, 151-158.

3.
H. Jung, Imaginary bicyclic function fields with the real cyclic subfield of class number one, Bull. Korean Math. Soc. 45 (2008), no. 2, 375-384.

4.
H. Jung, Hilbert 2-class field towers of imaginary quadratic function fields, J. Chungcheong Math. Soc. 23 (2010), no. 3, 547-553.

5.
F. Lemmermeyer, The 4-class group of real quadratic number fields, Preprint, 1998.

6.
C. Maire, Un raffinement du theoreme de Golod-Safarevic, Nagoya Math. J. 150 (1998), 1-11.

7.
J. Martinet, Tours de corps de classes et estimations de discriminants, Invent. Math. 44 (1978), no. 1, 65-73.

8.
M. Rosen, The Hilbert class field in function fields, Exposition. Math. 5 (1987), no. 4, 365-378.

9.
R. Schoof, Algebraic curves over \${\mathbb{F}}_2\$ with many rational points, J. Number Theory 41 (1992), no. 1, 6-14.