Abstract
We show that there are ≫ q l / ( 2 g ) \gg q^{l/(2g)} 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) has an element of order g g .
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