CLASS NUMBER DIVISIBILITY IN REAL QUADRATIC FUNCTION-FIELDS

Let q be a positive power of an odd prime p, and let F(q)(t) be the function field with coefficients in the finite field of q elements. Let h(F(q)(t, square-root M)) denote the ideal class number of the real quadratic function field obtained by adjoining the square root of an even-degree monic M is-an-element-of F(q)[t]. The following theorem is proved: Let n greater-than-or-equal-to 1 be an integer not divisible by p. Then there exist infinitely many monic, squarefree polynomials, M is-an-element-of F(q)[t] such that n divides the class number, h(F(q)(t, square-root M)). The proof constructs an element of order n in the ideal class group.