Malle's conjecture for fair counting functions

TL;DR

This paper investigates the applicability of Malle's conjecture to fair counting functions, revealing that a straightforward adaptation does not hold universally.

Contribution

It demonstrates that the naive extension of Malle's conjecture to fair counting functions is generally false.

Findings

Naive adaptation of Malle's conjecture fails in some cases

Provides counterexamples to the naive conjecture

Highlights the need for refined conjectural frameworks

Abstract

We show that the naive adaptation of Malle's conjecture to fair counting functions is not true in general.