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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 relative class number of cyclotomic function fields

Hwanyup Jung, Jaehyun Ahn (2003)

Acta Arithmetica

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 $f (T) \in 𝔽_{q} [T]$ 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 $P \in 𝔽_{q} [T]$ 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...

Displaying 1 – 12 of 12

A determinant formula for congruence zeta functions of maximal real cyclotomic function fields

A note on global units and local units of function fields

Class numbers of cyclotomic function fields

Digit derivatives and application to zeta measures

Greither's maximal independent system of units in global function fields

On ray class annihilators of cyclotomic function fields

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

On the relative class number of cyclotomic function fields

On the subfields of cyclotomic function fields

On the vanishing of Iwasawa invariants of geometric cyclotomic ℤₚ-extensions

Stickelberger elements in function fields

The Hasse-Witt invariant of cyclotomic function fields

Currently displaying 1 – 12 of 12