Class number parities of compositum of quadratic function fields

Abstract

Abstract The parities of ideal class numbers of compositum of quadratic function fields are studied. Especially, the parities of ideal class numbers of F q ( t ) ( P , Q ) and F q ( t ) ( P , Q , R ) $\mathbb{F}_q(t)(\sqrt P,\sqrt Q) \text{ and } \mathbb{F}_q(t)(\sqrt P,\sqrt Q,\sqrt R)$ are completely determined in detail, where P,Q,R are monic irreducible polynomials of even degrees.