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On the ordinarity of the maximal real subfield of cyclotomic function fields

Volume 165 / 2014

Daisuke Shiomi Acta Arithmetica 165 (2014), 225-242 MSC: Primary 11R60; Secondary 14H40. DOI: 10.4064/aa165-3-2


The aim of this paper is to clarify the ordinarity of cyclotomic function fields. In the previous work [J. Number Theory 133 (2013)], the author determined all monic irreducible polynomials $m$ such that the maximal real subfield of the $m$th cyclotomic function field is ordinary. In this paper, we extend this result to the general case.


  • Daisuke ShiomiDepartment of Mathematical Sciences
    Faculty of Science
    Yamagata University
    Kojirakawa-machi 1-4-12
    Yamagata 990-8560, Japan

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