• Title/Summary/Keyword: quadratic function

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ON CONTINUED FRACTIONS, FUNDAMENTAL UNITS AND CLASS NUMBERS OF REAL QUADRATIC FUNCTION FIELDS

  • Kang, Pyung-Lyun
    • Journal of the Chungcheong Mathematical Society
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    • v.27 no.2
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    • pp.183-203
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    • 2014
  • We examine fundamental units of quadratic function fields from continued fraction of $\sqrt{D}$. As a consequence, we give another proof of geometric analog of Ankeny-Artin-Chowla-Mordell conjecture and bounds for class number, and study real quadratic function fields of minimal type with quasi-period 4.

HILBERT 2-CLASS FIELD TOWERS OF IMAGINARY QUADRATIC FUNCTION FIELDS

  • Ahn, Jaehyun;Jung, Hwanyup
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.4
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    • pp.699-704
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    • 2010
  • In this paper, we prove that the Hilbert 2-class field tower of an imaginary quadratic function field $F=k({\sqrt{D})$ is infinite if $r_2({\mathcal{C}}(F))=4$ and exactly one monic irreducible divisor of D is of odd degree, except for one type of $R{\acute{e}}dei$ matrix of F. We also compute the density of such imaginary quadratic function fields F.

ON HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS

  • Jung, Hwanyup
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.3
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    • pp.547-553
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    • 2010
  • In this paper we prove that real quadratic function field F over ${\mathbb{F}}_q(T)$ has infinite 2-class field tower if the 4-rank of narrow ideal class group of F is equal to or greater than 4 when $q{\equiv}3$ mod 4.

REAL QUADRATIC FUNCTION FIELDS OF MINIMAL TYPE

  • Byeon, Dongho;Keem, Jiae;Lee, Sangyoon
    • Communications of the Korean Mathematical Society
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    • v.28 no.4
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    • pp.735-740
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    • 2013
  • In this paper, we will introduce the notion of the real quadratic function fields of minimal type, which is a function field analogue to Kawamoto and Tomita's notion of real quadratic fields of minimal type. As number field cases, we will show that there are exactly 6 real quadratic function fields of class number one that are not of minimal type.