On the relative class number of cyclotomic function fields

Class numbers of some abelian extensions of rational function fields

“…In this paper we generalize the Bae-Kang determinant formula for h(K + P n ) and the Jung-Ahn formula for h − (K P n ) to any subfield K of K P n . Our proof is much simpler than the proofs of [BK] and [JA1].…”

“…In a recent paper Bae and Kang [BK] have obtained determinant formulas for h − (K P n ) and h(K + P n ), where P is a monic irreducible polynomial in A. In [JA1], Jung and Ahn have obtained a determinant formula for h − (K P n ). In this paper we generalize the Bae-Kang determinant formula for h(K + P n ) and the Jung-Ahn formula for h − (K P n ) to any subfield K of K P n .…”

On the size of determinants in the class number formulae of cyclotomic function fields

“…In this article, we discuss the size of the determinants of specific 0/1 (or ±1) matrices, which appear in the determinant formula of the relative class numbers of cyclotomic function fields. This determinant formula was proved by Jung-Ahn [1,2].…”

“…On the other hand, when q > 3,h − m is no longer huge (Table 2). We calculate 100, 000 samples of randomly generated symmetric 0/1 matrices of the same size as in the determinant formula (2). This computation had been performed by our program written in C using Pari library [6].…”

Determinant formulas for class numbers in function fields

“…In the function field case, some determinant formulas involving the relative class number and the real class number of cyclotomic function fields with prime power conductors are obtained by several authors (Rosen [9], Bae-Kang [3] and Jung-Ahn [6,7]). Recently the authors gave determinant formulas for the real and relative class number of any subfield of a cyclotomic field with prime power conductor [2].…”