Article ID Journal Published Year Pages File Type
4595203 Journal of Number Theory 2007 8 Pages PDF
Abstract

Let q be a power of an odd prime number p and K:=Fq(T) be the rational function field with a fixed indeterminate T. For P a prime of K, let be the maximal real subfield of the Pth-cyclotomic function field and its ring of integers. We prove that there exists infinitely many primes P of even degree such that the cardinal of the ideal class group is divisible by q. We prove also an analogous result for imaginary extensions.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory