scholarly journals Real quadratic function fields of Richaud-Degert type with ideal class number one

2012 ◽  
Vol 140 (2) ◽  
pp. 403-414 ◽  
Author(s):  
Sunghan Bae
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Quadratic Function ◽  
Ideal Class ◽  
Quadratic Function Fields ◽  
Real Quadratic

Class Number Divisibility in Real Quadratic Function Fields

1992 ◽  
Vol 35 (3) ◽  
pp. 361-370 ◽  
Author(s):  
Christian Friesen
Keyword(s):  
Class Number ◽  
Function Field ◽  
Class Group ◽  
Quadratic Function ◽  
Ideal Class ◽  
Ideal Class Group ◽  
Quadratic Function Field ◽  
Quadratic Function Fields ◽  
Real Quadratic ◽  
The Ideal

AbstractLet q be a positive power of an odd prime p, and let Fq(t) be the function field with coefficients in the finite field of q elements. Let denote the ideal class number of the real quadratic function field obtained by adjoining the square root of an even-degree monic . The following theorem is proved: Let n ≧ 1 be an integer not divisible by p. Then there exist infinitely many monic, squarefree polynomials, such that n divides the class number, . The proof constructs an element of order n in the ideal class group.

Class number parities of compositum of quadratic function fields

2017 ◽  
Vol 67 (2) ◽  
Author(s):  
Sunghan Bae ◽  
Hwanyup Jung
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Quadratic Function ◽  
Class Numbers ◽  
Ideal Class ◽  
Quadratic Function Fields

AbstractThe parities of ideal class numbers of compositum of quadratic function fields are studied. Especially, the parities of ideal class numbers of

A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn

2006 ◽  
Vol 49 (3) ◽  
pp. 448-463 ◽  
Author(s):  
Allison M. Pacelli
Keyword(s):  
Lower Bound ◽  
Class Number ◽  
Function Fields ◽  
Quadratic Function ◽  
Class Numbers ◽  
Prime Degree ◽  
Cyclic Function ◽  
Quadratic Function Fields

AbstractIn this paper, we find a lower bound on the number of cyclic function fields of prime degreelwhose class numbers are divisible by a given integern. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible byn.

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