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

Daisuke Shiomi (2014)

Acta Arithmetica

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 mth cyclotomic function field is ordinary. In this paper, we extend this result to the general case.

On the subfields of cyclotomic function fields

Zhengjun Zhao, Xia Wu (2013)

Czechoslovak Mathematical Journal

Let K = 𝔽 q ( T ) be the rational function field over a finite field of q elements. For any polynomial f ( T ) 𝔽 q [ T ] with positive degree, denote by Λ f the torsion points of the Carlitz module for the polynomial ring 𝔽 q [ T ] . In this short paper, we will determine an explicit formula for the analytic class number for the unique subfield M of the cyclotomic function field K ( Λ P ) of degree k over 𝔽 q ( T ) , where P 𝔽 q [ T ] is an irreducible polynomial of positive degree and k > 1 is a positive divisor of q - 1 . A formula for the analytic class number for the...

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