IMAGINARY BICYCLIC FUNCTION FIELDS WITH THE REAL CYCLIC SUBFIELD OF CLASS NUMBER ONE

Title & Authors
IMAGINARY BICYCLIC FUNCTION FIELDS WITH THE REAL CYCLIC SUBFIELD OF CLASS NUMBER ONE
Jung, Hwan-Yup;

Abstract
Let $\small{k={\mathbb{F}}_q(T)}$ and $\small{{\mathbb{A}}={\mathbb{F}}_q[T]}$. Fix a prime divisor $\small{{\ell}}$ q-1. In this paper, we consider a $\small{{\ell}}$-cyclic real function field $\small{k(\sqrt[{\ell}]P)}$ as a subfield of the imaginary bicyclic function field K = $\small{k(\sqrt[{\ell}]P,\;(\sqrt[{\ell}]{-Q})}$, which is a composite field of $\small{k(\sqrt[{\ell}]P)}$ wit a $\small{{\ell}}$-cyclic totally imaginary function field $\small{k(\sqrt[{\ell}]{-Q})}$ of class number one. und give various conditions for the class number of $\small{k(\sqrt[{\ell}]{P})}$ to be one by using invariants of the relatively cyclic unramified extensions $\small{K/F_i}$ over $\small{{\ell}}$-cyclic totally imaginary function field $\small{F_i=k(\sqrt[{\ell}]{-P^iQ})}$ for $\small{1{\leq}i{\leq}{\ell}-1}$
Keywords
imaginary bicyclic function field;real cyclic function field;class number one;
Language
English
Cited by
1.
ON HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS,;

충청수학회지, 2010. vol.23. 3, pp.547-553
2.
HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS,;

대한수학회논문집, 2014. vol.29. 2, pp.219-226
1.
HILBERT 2-CLASS FIELD TOWERS OF REAL QUADRATIC FUNCTION FIELDS, Communications of the Korean Mathematical Society, 2014, 29, 2, 219
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