Class number of (v, n, M)-extensions
Osama Alkam, Mehpare Bilhan · Bulletin of the Australian Mathematical Society · 2001
An analogue of cyclotomic number fields for function fields over the finite field q, was investigated by L. Carlitz in 1935 and has been studied recently by D. Hayes, M. Rosen, S. Galovich and others. For each nonzero polynomial M in q [T], we denote by k (ΛM) the cyclotomic function field associated with M, where k = q(T). Replacing T by 1/T in k and considering the cyclotomic function field Fv that corresponds to (1/T)v+1 gets us an extension of k, denoted by Lv, which is the fixed field of Fv modulo . We define a (v, n, M)-extension to be the composite N = knk (Λm) Lv where kn is the constant field of degree n over k. In this paper we give analytic class number formulas for (v, n, M)-extensions when M has a nonzero constant term.