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A NOTE ON CYCLOTOMIC UNITS IN FUNCTION FIELDS
Hwan yup Jung 충청수학회 2007 충청수학회지 Vol.20 No.4
Let A = Fq[T] and k = Fq(T). Assume q is odd, and ¯xa prime divisor ` of q ¡1. Let P be a monic irreducible polynomial in A whose degree d is divisible by `. In this paper we de¯ne a subgroup e CF of O¤F which is generated by F¤q and f´¿i: 0 · i ·` ¡ 1g in F = k( `pP) and calculate the unit-index [O¤F : e CF ] =``¡2h(OF ). This is a generalization of [3, Theorem 16.15].
ON HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS
Hwan yup Jung 충청수학회 2010 충청수학회지 Vol.23 No.3
In this paper we prove that real quadratic function ¯eld F over Fq(T) has in¯nite 2-class ¯eld tower if the 4-rank of narrow ideal class group of F is equal to or greater than 4 when q ´ 3 mod 4.
THAINE’S THEOREM IN FUNCTION FIELD
Hwan yup Jung 충청수학회 2009 충청수학회지 Vol.22 No.1
Let F be a finite real abelian extension of a global function field k with G = Gal(F/k). Assume that F is an extension field of the Hilbert class field Ke of k and is contained in a cyclotomic function field Kn. Let ` be any prime number not dividing phk|G|. In this paper, we show that if 2 Z[G] annihilates the Sylow `-subgroup of O×F /CF, then (q−1) annihilates the Sylow `-subgroup of ClF.
IMAGINARY BICYCLIC FUNCTION FIELDS WITH THE REAL CYCLIC SUBFIELD OF CLASS NUMBER ONE
Jung, Hwan-Yup Korean Mathematical Society 2008 대한수학회보 Vol.45 No.2
Let $k={\mathbb{F}}_q(T)$ and ${\mathbb{A}}={\mathbb{F}}_q[T]$. Fix a prime divisor ${\ell}$ q-1. In this paper, we consider a ${\ell}$-cyclic real function field $k(\sqrt[{\ell}]P)$ as a subfield of the imaginary bicyclic function field K = $k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})$, which is a composite field of $k(\sqrt[{\ell}]P)$ wit a ${\ell}$-cyclic totally imaginary function field $k(\sqrt[{\ell}]{-Q})$ of class number one. und give various conditions for the class number of $k(\sqrt[{\ell}]{P})$ to be one by using invariants of the relatively cyclic unramified extensions $K/F_i$ over ${\ell}$-cyclic totally imaginary function field $F_i=k(\sqrt[{\ell}]{-P^iQ})$ for $1{\leq}i{\leq}{\ell}-1$.
DETERMINATION OF ALL SUBFIELDS OF CYCLOTOMIC FUNCTION FIELDS WITH GENUS ONE
JUNG, HWAN-YUP,AHN, JAE-HYUN Korean Mathematical Society 2005 대한수학회논문집 Vol.20 No.2
In this paper we determine all subfields with genus one of cyclotomic function fields over rational function fields explicitly.
8-RANKS OF CLASS GROUPS OF IMAGINARY QUADRATIC NUMBER FIELDS AND THEIR DENSITIES
Jung, Hwan-Yup,Yue, Qin Korean Mathematical Society 2011 대한수학회지 Vol.48 No.6
For imaginary quadratic number fields F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1{\ldots}p_{t-1}})$, where ${\varepsilon}{\in}${-1,-2} and distinct primes $p_i{\equiv}1$ mod 4, we give condition of 8-ranks of class groups C(F) of F equal to 1 or 2 provided that 4-ranks of C(F) are at most equal to 2. Especially for F = $\mathbb{Q}(\sqrt{{\varepsilon}p_1p_2)$, we compute densities of 8-ranks of C(F) equal to 1 or 2 in all such imaginary quadratic fields F. The results are stated in terms of congruence relation of $p_i$ modulo $2^n$, the quartic residue symbol $(\frac{p_1}{p_2})4$ and binary quadratic forms such as $p_2^{h+(2_{p_1})/4}=x^2-2p_1y^2$, where $h+(2p_1)$ is the narrow class number of $\mathbb{Q}(\sqrt{2p_1})$. The results are also very useful for numerical computations.
GROUP DETERMINANT FORMULAS AND CLASS NUMBERS OF CYCLOTOMIC FIELDS
Jung, Hwan-Yup,Ahn, Jae-Hyun Korean Mathematical Society 2007 대한수학회지 Vol.44 No.3
Let m, n be positive integers or monic polynomials in $\mathbb{F}_q[T]$ with n|m. Let $K_m\;and\;K^+_m$ be the m-th cyclotomic field and its maximal real subfield, respectively. In this paper we define two matrices $D^+_{m,n}\;and\;D^-_{m,n}$ whose determinants give us the ratios $\frac{h(\mathcal{O}_{K^+_m})}{h(\mathcal{O}_{K^+_n})}$ and $\frac{h-(\mathcal{O}_K_m)}{h-(\mathcal{O}_K_n)}$ with some factors, respectively.
Enhanced Display of Lipase on the Escherichia coli Cell Surface, Based on Transcriptome Analysis
Baek, Jong Hwan,Han, Mee-Jung,Lee, Seung Hwan,Lee, Sang Yup American Society for Microbiology 2010 Applied and environmental microbiology Vol.76 No.3
<B>ABSTRACT</B><P>A cell surface display system was developed using <I>Escherichia coli</I> OmpC as an anchoring motif. The fused <I>Pseudomonas fluorescens</I> SIK W1 lipase was successfully displayed on the surface of <I>E. coli</I> cells, and the lipase activity could be enhanced by the coexpression of the <I>gadBC</I> genes identified by transcriptome analysis.</P>