... Annals of Mathematics, 159 (2004), 217–250 Higher composition laws I: A new view on Gauss composition, and quadratic generalizations By Manjul Bhargava Introduction Two centuries ago, in ... 2a0 a2 + a0 a1 a3 − ε a1 ), − (a1 a2 − 2a2 a3 + a0 a2 a3 + ε a2 ), 2 − 3a a a + a a2 + ε a ), − ( 2a2 3 c0 = c1 = c2 = c3 = where as usual ε = or in accordance with whether D ≡ or modulo (Again, ... new laws of composition These laws of composition are defined on 1) binary cubic forms, 2) pairs of binary quadratic forms, 3) pairs of quaternary alternating 2-forms, and 4) senary (six-variable)...