Decomposition of places in dihedral and cyclic quintic trinomial extensions of global fields

Im, Boe-Hae; Lee, Yoonjin

doi:10.1007/s00229-011-0459-4

manuscripta math.

2011

DOI: 10.1007/s00229-011-0459-4

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Decomposition of places in dihedral and cyclic quintic trinomial extensions of global fields

Boe-Hae Im

Yoonjin Lee

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2017

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Regulators of an Infinite Family of the Simplest Quartic Function Fields

Lee¹,

Lee²

2017

Can. j. math.

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Abstract. We explicitly nd regulators of an in nite family {L m } of the simplest quartic function elds with a parameter m in a polynomial ring F q [t], where F q is thenite eld of order q with odd characteristic. In fact, this in nite family of the simplest quartic function elds are sub elds of maximal real sub elds of cyclotomic function elds, where they have the same conductors. We obtain a lower bound on the class numbers of the family {L m } and some result on the divisibility of the divisor class numbers of cyclotomic function elds which contain {L m } as their sub elds. Furthermore, we nd an explicit criterion for the characterization of splitting types of all the primes of the rational function eld F q (t) in {L m }.

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Regulators of an Infinite Family of the Simplest Quartic Function Fields

Lee¹,

Lee²

2017

Can. j. math.

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show abstract

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Decomposition of places in dihedral and cyclic quintic trinomial extensions of global fields

Cited by 1 publication

References 11 publications

Regulators of an Infinite Family of the Simplest Quartic Function Fields

Regulators of an Infinite Family of the Simplest Quartic Function Fields

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