 By definition, this is a coset of K modulo U. Arf showed that indeed Arf(formula_13) does not change if formula_13 is replaced by an equivalent quadratic form, which is to say that it is an invariant of formula_13.The Arf invariant is additive; in other words, the Arf invariant of an orthogonal sum of two quadratic forms is the sum of their Arf invariants.For a field "K" of characteristic 2, Artin-Schreier theory identifies the quotient group of "K" by the subgroup "U" above with the Galois cohomology group "H"1("K", F2).