An invariance property of Hankel forms

Abstract

For an extension k( x)/ k( y) of rational function fields one can define, when y(∞)≠∞, a nondegenerate bilinear form H x, y of dimension n = [ k( x: k( y)]; we call it a Hankel form, since its matrix is the Hankel matrix of the development of y = g( x)/ h( x) at ∞. We show that Hankel forms behave under the action of PGl 2( k) as follows: H λ( x),μ( y) ≅detλ·detμ· H x, y·