On constructing fields corresponding to the 𝐴̃_{𝑛}’s of Mestre for odd 𝑛

Abstract

Abstract. An isomorphism is given between the trace bilinear form of Mestre's An extensions over Q(t) and a certain quadratic form over Q with base field lifted to Q(<). This reduces the problem of constructing Än extensions from Mestre's An 's to that of diagonalizing certain forms over Q. The result expands a result of Schneps.