Regulators and class numbers of an infinite family of quintic function fields

2018 ◽  
Vol 185 (2) ◽  
pp. 107-125
Author(s):  
Jungyun Lee ◽  
Yoonjin Lee

2017 ◽  
Vol 69 (3) ◽  
pp. 579-594 ◽  
Author(s):  
Jungyun Lee ◽  
Yoonjin Lee

AbstractWe explicitly find regulators of an infinite family {Lm} of the simplest quartic function fields with a parameter m in a polynomial ring [t], where is the finite field of order q with odd characteristic. In fact, this infinite family of the simplest quartic function fields are subfields of maximal real subfields of cyclotomic function fields having the same conductors. We obtain a lower bound on the class numbers of the family {Lm} and some result on the divisibility of the divisor class numbers of cyclotomic function fields that contain {Lm} as their subfields. Furthermore, we find an explicit criterion for the characterization of splitting types of all the primes of the rational function field (t) in {Lm}.





1975 ◽  
Vol 28 (2) ◽  
pp. 111-114 ◽  
Author(s):  
Lawrence Washington


2004 ◽  
Vol 74 (250) ◽  
pp. 953-966 ◽  
Author(s):  
Hwanyup Jung ◽  
Sunghan Bae ◽  
Jaehyun Ahn


2006 ◽  
Vol 49 (3) ◽  
pp. 448-463 ◽  
Author(s):  
Allison M. Pacelli

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.







Sign in / Sign up

Export Citation Format

Share Document