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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2019; 56(2): 559-578

Online first article February 12, 2019      Printed March 1, 2019

https://doi.org/10.4134/JKMS.j180279

Copyright © The Korean Mathematical Society.

Cylotomic function fields over finite fields with class number three

Mehpare Bilhan, Dilek Buyruk, Ferruh Ozbudak

Middle East Technical University; Abant Izzet Baysal University; Middle East Technical University

Abstract

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We list all subfields of cyclotomic function fields over rational function fields with class number three. We also determine all the imaginary abelian extensions with relative class number three, explicitly.

Keywords: class number, cyclotomic function field, L-polynomial

MSC numbers: 11R29, 11R60, 12E20

Supported by: The third author was partially supported by TUBITAK under Grant No. TBAG-109T672.

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