On real quadratic function fields Original Research Article

Let q be a power of an odd prime number p and image be the rational function field with a fixed indeterminate T. For P a prime of K, let image be the maximal real subfield of the Pth-cyclotomic function field and image 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 image is divisible by q. We prove also an analogous result for imaginary extensions.