Exponents of Class Groups of Quadratic Function Fields over Finite Fields

Abstract

AbstractWe find a lower bound on the number of imaginary quadratic extensions of the function fieldwhose class groups have an element of a fixed order.More precisely, letq≥ 5 be a power of an odd prime and letgbe a fixed positive integer ≥ 3. There arepolynomialsD∈with deg(D) ≤ℓsuch that the class groups of the quadratic extensionshave an element of orderg.