# Higher Composition Law

Prof M.Bhargava's work on "Higher Composition Law" which solved some outstanding conjectures on number theory seems to be very interesting topic. I have seen his papers but, in spite of the titles, it is not easy to understand (Of course in my point of view, for sure there are many people who can understand it easily).

Do you know any lecture note or expository paper which explains more details and some explicit example? especially his work on composition law for binary quadratic form.

Thanks

• Have you looked at his ICM notes or notes in this Algorithmic Number Theory Volume? His composition law for binary quadratic forms is of course the same as Gauss's. However, one new thing was a composition law on triples of binary quadratic forms. – Kimball Nov 8 '10 at 14:08

• @Franz: I think according to Theorem 1 of Bhargava's paper "Higher composition laws I" if $Q_{id,D}$ be any primitive binary quadratic form of discriminant $D$ such that there is a cube $A_0$ with $Q^{A0}_1= Q^{A0}_2=Q^{A0}_3=Q_{id,D}$ then there is a unique group law. For an specific $Q_{id,D}$ one can get usual Guass Composition Law. It seems that you have picked this specific case. I might be confused. – M.B Nov 9 '10 at 7:03