Jaehyun Ahn

CLASS NUMBER FORMULAE IN THE FORM OF A PRODUCT OF DETERMINANTS IN FUNCTION FIELDS

In this paper, we generalize the Kuceras group-determinant formulae to obtain the real and relative class number formulae of any subfield of cyclotomic function fields with arbitrary conductor in the form of a product of determinants. From these formulae, we generalize the relative class number formula of Rosen and Bae-Kang and obtain analogous results of Tsumura and Hirabayashi for an intermediate field in the tower of cyclotomic function fields with prime power conductor.

Cyclotomic units and Stickelberger ideals of global function fields

In this paper, we define the group of cyclotomic units and Stickelberger ideals in any subfield of the cyclotomic function field. We also calculate the index of the group of cyclotomic units in the total unit group in some special cases and the index of Stickelberger ideals in the integral group ring.

Demjanenko matrix and recursion formula for relative class number over function fields

Abstract In this paper, we define Demjanenko matrix in function field and express the relative ideal class numbers h − ( O K P n ) as the determinant of this matrix. We also define another matrix which give us a recursion formula for the relative divisor class numbers h−(KPn).

Class numbers of some abelian extensions of rational function fields

Let P be a monic irreducible polynomial. In this paper we generalize the determinant formula for h(K+pn) of Bae and Kang and the formula for h-(Kpn) of Jung and Ahn to any subfields K of the cyclotomic function field Kpn. By using these formulas, we calculate the class numbers h-(K), h(k+) of all subfields K of Kp when q and deg(P) are small.

CYCLOTOMIC UNITS AND DIVISIBILITY OF THE CLASS NUMBER OF FUNCTION FIELDS

Let ＝(T) be a rational function field. Let be a prime number with (, q-1) ＝ 1. Let K/ be an elmentary abelian -extension which is contained in some cyclotomic function field. In this paper, we study the -divisibility of ideal class number of K by using cyclotomic units.s.s.

A DETERMINANT FORMULA FOR CONGRUENT ZETA FUNCTIONS OF REAL ABELIAN FUNCTION FIELDS

Abstract. In this paper we give a determinant formula for congruentzeta functions of real Abelian function elds. We also give some examplesof congruent zeta functions when the conductor of real Abelian function eld is monic irreducible. 1. IntroductionLet k = F q ( T ) be the rational function eld over the nite eld F q andA = F q [ T ]. Let 1 be the place of k associated to 1 =T , which is called thein nite one of k. Write A + = f 1 = M 2 A : M is monic g and A +irr = fP 2 A + : P is irreducible g . For any M 2 A + , write K M for the M th cyclotomicfunction eld and K + M for the maximal real sub eld of K M . In this paper, byan Abelian function eld , we always mean a nite Abelian extension F of kwhich is contained in a cyclotyomic function eld K M , and F is said to be real if 1 splits completely in F . Let N = N ( F ) 2 A + be the conductor of F , thatis, K N is the smallest cyclotomic function eld containing F . For such a eld F , there exists a polynomial P F ( X ) 2 Z[

DETERMINATION OF ALL SUBFIELDS OF CYCLOTOMIC FUNCTION FIELDS WITH DIVISOR CLASS NUMBER TWO

In this paper, we determine all subfields of cyclotomic function fields with divisor class number two. We also give the generators of such fields explicitly.

KUCERA GROUP OF CIRCULAR UNITS IN FUNCTION FIELDS

Let [T] be the polynomial ring over a finite field [T] and K=(T) its field of fractions. Let be a fixed prime divisor of q-1. Let J be a finite set of monic irreducible polynomials with deg (mod . In this paper we define the group of circular units in K=k in the sense of Kucera [4] and compute the index of in the full unit group .

DETERMINATION OF ALL SUBFIELDS OF CYCLOTOMIC FUNCTION FIELDS WITH GENUS ONE

In this paper we determine all subfields with genus one of cyclotomic function fields over rational function fields explicitly.

Maximal independent system of units in function fields

In this paper, we construct a new maximal independent system of units in cyclotomic function fields and their subfields. We also calculate its index in the full units group and show that it is smaller than the index of Feng-Yins system.