On the Class Numbers of the Maximal Real Subfields of Cyclotomic Function Fields, II Original Research Article

Letqbe a power of a prime numberpandk=imageq(T) the rational function field with a fixed indeterminateT. For an irreducible monic image=image(T) inR=imageq[T], letk(image)+be the maximal real subfield of the imageth cyclotomic function field andh+T(image) the class number ofk(image)+associated toR. We prove that there exist infinitely many irreducible monics image inRwithp h+T(image) under some assumptions onq.