CLASS NUMBER DIVISIBILITY OF QUADRATIC FUNCTION FIELDS IN EVEN CHARACTERISTIC

Title & Authors
CLASS NUMBER DIVISIBILITY OF QUADRATIC FUNCTION FIELDS IN EVEN CHARACTERISTIC
Bae, Sunghan; Jung, Hwanyup;

Abstract
We find a lower bound on the number of real/inert imagi-nary/ramified imaginary quadratic extensions of the function field $\small{\mathbb{F}_q(t)}$ whose ideal class groups have an element of a fixed order, where $\small{q}$ is a power of 2.
Keywords
class number divisibility;quadratic function field;even characteristic;
Language
English
Cited by
References
1.
S. Bae, Real quadratic function fields of Richaud-Degert type with ideal class number one, Proc. Amer. Math. Soc. 140 (2012), no. 2, 403-414.

2.
D. A. Cardon and M. R. Murty, Exponents of class groups of quadratic function fields over finite fields, Canad. Math. Bull. 44 (2001), no. 4, 398-407.

3.
K. Chakraborty and A. Mukhopadhyay, Exponents of class groups of real quadratic function fields, Proc. Amer. Math. Soc. 132 (2004), no. 7, 1951-1955.

4.
C. Friesen, Class number divisibility in real quadratic function fields, Canad. Math. Bull. 35 (1992), no. 3, 361-370.

5.
R. Murty, Exponents of class groups of quadratic fields, Topics in number theory (University Park, PA, 1997), 229-239, Math. Appl., 467, Kluwer Acad. Publ., Dordrecht, 1999.

6.
R. J. Zuccherato, The continued fraction algorithm and regulator for quadratic function fields of characteristic 2, J. Algebra 190 (1997), no. 2, 563-587.