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On the subfields of cyclotomic function fields

Zhengjun ZhaoXia 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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