Montesinos Amilibia, José María2023-06-202023-06-2020130018-2079https://hdl.handle.net/20.500.14352/44490Addendum to ‘‘On integral quadratic forms having commensurable groups of automorphisms’’, disponible en http://projecteuclid.org/euclid.hmj/1419619751We introduce two notions of equivalence for rational quadratic forms. Two n-ary rational quadratic forms are commensurable if they possess commensurable groups of automorphisms up to isometry. Two n-ary rational quadratic forms F and G are projectivelly equivalent if there are nonzero rational numbers r and s such that rF and sG are rationally equivalent. It is shown that if F\ and G\ have Sylvester signature {−,+,+,...,+} then F\ and G\ are commensurable if and only if they are projectivelly equivalent. The main objective of this paper is to obtain a complete system of (computable) numerical invariants of rational n-ary quadratic forms up to projective equivalence. These invariants are a variation of Conway's p-excesses. Here the cases n odd and n even are surprisingly different. The paper ends with some examplesengjournal articlehttp://projecteuclid.org/euclid.hmj/1389102581open access515.111E04: Quadratic forms over general fields 11E20: General ternary and quaternary quadratic formsforms of more than two variables 57M25: Knots and links in S3 {For higher dimensionssee 57Q45} 57M50: Geometric structures on low-dimensional manifolds 57M60: Group actions in low dimensionsTopología1210 Topología