Even quadratic forms with cube-free discriminant
Donald G. James · Proceedings of the American Mathematical Society · 1989
A formula is given for the number of genera of even lattices with rank n n , signature s s , and discriminant ( − 1 ) ( n − s ) / 2 d 2 D {( - 1)^{(n - s)/2}}{d^2}D , when d D dD is odd and square-free. In the indefinite case, an orthogonal splitting of these lattices into simple components is also determined.