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arXiv · 2502.04261

Counterexamples for T\"urkelli's Modification on Malle's Conjecture

Jiuya Wang
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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 $b$ 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 $b$ for number fields.

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Jiuya Wang. 2025-02-06. Counterexamples for T\"urkelli's Modification on Malle's Conjecture. https://arxiv.org/abs/2502.04261

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