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
Keyword(s):  
Function Fields ◽  
Infinite Family ◽  
Class Numbers

Regulators of an Infinite Family of the Simplest Quartic Function Fields

2017 ◽  
Vol 69 (3) ◽  
pp. 579-594 ◽  
Author(s):  
Jungyun Lee ◽  
Yoonjin Lee
Keyword(s):  
Lower Bound ◽  
Finite Field ◽  
Polynomial Ring ◽  
Function Fields ◽  
Infinite Family ◽  
Class Numbers ◽  
Explicit Criterion ◽  
Divisor Class ◽  
The Family

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}.

scholarly journals An infinite family of pairs of imaginary quadratic fields with both class numbers divisible by five

2017 ◽  
Vol 176 ◽  
pp. 333-343 ◽  
Author(s):  
Miho Aoki ◽  
Yasuhiro Kishi
Keyword(s):  
Infinite Family ◽  
Quadratic Fields ◽  
Class Numbers ◽  
Imaginary Quadratic Fields

scholarly journals Class numbers of elliptic function fields and the distribution of prime numbers

1975 ◽  
Vol 28 (2) ◽  
pp. 111-114 ◽  
Author(s):  
Lawrence Washington
Keyword(s):  
Elliptic Function ◽  
Function Fields ◽  
Prime Numbers ◽  
Class Numbers

scholarly journals Determinant formulas for class numbers in function fields

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

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.

scholarly journals Divisibility of class numbers of imaginary quadratic function fields by a fixed odd number

2013 ◽  
Vol 123 (1) ◽  
pp. 1-18
Author(s):  
PRADIPTO BANERJEE ◽  
SRINIVAS KOTYADA
Keyword(s):  
Function Fields ◽  
Quadratic Function ◽  
Class Numbers ◽  
Quadratic Function Fields

scholarly journals On the Class Numbers of the Maximal Real Subfields of Cyclotomic Function Fields

1998 ◽  
Vol 4 (2) ◽  
pp. 167-174 ◽  
Author(s):  
Humio Ichimura
Keyword(s):  
Function Fields ◽  
Class Numbers
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