Analytic class number formulas in function fields

1981 ◽  
Vol 65 (1) ◽  
pp. 49-69 ◽  
Author(s):  
David R. Hayes
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Analytic Class

scholarly journals A Class Number Relation Over Function Fields

1995 ◽  
Vol 54 (2) ◽  
pp. 318-340 ◽  
Author(s):  
J.K. Yu
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Number Relation

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 Function fields of class number one

2015 ◽  
Vol 154 ◽  
pp. 375-379 ◽  
Author(s):  
Qibin Shen ◽  
Shuhui Shi
Keyword(s):  
Class Number ◽  
Function Fields

On the class number of the lpth cyclotomic number field

1991 ◽  
Vol 109 (2) ◽  
pp. 263-276
Author(s):  
Norikata Nakagoshi
Keyword(s):  
Number Field ◽  
Class Number ◽  
Prime Factor ◽  
Analytic Formula ◽  
Cyclotomic Number ◽  
Class Number Formula ◽  
Prime Factors ◽  
Number Formula ◽  
Genus Number ◽  
Analytic Class

The first factor of the class number of a cyclotomic number field can be obtainable by the analytic class number formula and there are some tables which show the decompositions of the first factors into primes. But, using just the analytic formula, we cannot tell what kinds of primes will appear as the factors of the class number of a given cyclotomic number field, except for those of the genus number, or the irregular primes. It is significant to find in advance the prime factors, particularly those prime to the degree of the field. For instance, in the table of the first factors we can pick out some pairs (l, p) of two odd primes l and p such that the class number of each lpth cyclotomic number field is divisible by l even if p 1 (mod l). If p ≡ (mod l) for l ≥ 5 or p ≡ 1 (mod 32) for l = 3, then it is easy from the outset to achieve our intention of finding the factor l using the genus number formula. Otherwise it seems to be difficult. We wish to make it clear algebraically why the class number has the prime factor l.

scholarly journals Cyclotomic Function Fields with Divisor Class Number One

1991 ◽  
Vol 14 (1) ◽  
pp. 45-56 ◽  
Author(s):  
Masanari KIDA ◽  
Naoki MURABAYASHI
Keyword(s):  
Class Number ◽  
Function Fields ◽  
Divisor Class
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