Genera And The Class Group
H E Rose · 1995
Abstract We begin by introducing the equivalence of forms modulo a prime (that is. studying forms locally; see Section 3 of Chapter 3), this gives a new class structure with classes called genera. Secondly, we will show that the set of equivalence classes (in the original sense) forms a group, called the class group, under the operation of composition of forms defined below. The genera are cosets of this group and this fact enables us to derive some arithmetical properties of the class group. Finally, we give a formula for h(d), the order of the class group for discriminant d.