L-Functions of Carlitz modules, resultantal varieties and rooted binary trees, II

Abstract

We continue study of some algebraic varieties (called resultantal varieties) started in a paper of authors “L-functions of Carlitz modules, resultantal varieties and rooted binary trees, I”, cited as [4]. These varieties are related with the Sylvester matrix for the resultant of two polynomials, from one side, and with the L-functions of twisted Carlitz modules, from another side. They are described in terms of weighted rooted binary trees. We give some proofs that lack in [4], some examples and tables that confirm conjectures from [4], and some ideas of development of this theory.