Exponents of class groups of real quadratic function fields (II)

Abstract

Let g g be an even positive integer. We show that there are ≫ q l / g / l 2 \gg q^{l/g}/l^2 polynomials D ∈ F q [ t ] D\in \mathbb F_q[t] with deg ⁡ ( D ) ≤ l \deg (D)\le l such that the ideal class group of the real quadratic extensions F q ( t , D ) \mathbb F_q(t,\sqrt D) have an element of order g g .