Explicit statement of a conjecture on resultantal varieties

TL;DR

This paper explicitly states a conjecture about the equality of certain resultantal varieties related to L-functions of Carlitz modules, formulated through polynomial ideal membership, and provides initial numerical evidence.

Contribution

It formulates a precise conjecture connecting resultantal varieties and polynomial ideals in the context of Carlitz modules, with supporting numerical results.

Findings

Explicit conjecture on resultantal varieties

Numerical evidence supporting the conjecture

Polynomial ideal membership formulation

Abstract

The paper [GLZ] "L-functions of Carlitz modules, resultantal varieties and rooted binary trees" is devoted to a description of some resultantal varieties related to L-functions of Carlitz modules. It contains a conjecture that some of these varieties coincide. This conjecture can be formulated in terms of polynomials, namely, in terms of a fact that an explicitly defined polynomial belongs to the radical of the ideal generated by some other polynomials. We give an explicit statement of this conjecture and a numerical result.