Counterexamples for T\"urkelli's Modification on Malle's Conjecture
Number Theory
2025-04-08 v2
Abstract
We give counterexamples for the modification on Malle's Conjecture given by T\"urkelli. T\"urkelli's modification on Malle's conjecture is inspired by an analogue of Malle's conjecture over a function field. As a consequence, our counterexamples demonstrate that the constant can differ between function fields and number fields. We also show that Kl\"uners' counterexamples give counterexamples for a natural extension of Malle's conjecture to counting number fields by product of ramified primes. We then propose a refined version of Malle's conjecture which implies a new conjectural value for the constant for number fields.
Cite
@article{arxiv.2502.04261,
title = {Counterexamples for T\"urkelli's Modification on Malle's Conjecture},
author = {Jiuya Wang},
journal= {arXiv preprint arXiv:2502.04261},
year = {2025}
}