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arXiv · 2211.16698

Malle's conjecture with multiple invariants

Fabian Gundlach
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Abstract

We define invariants $\operatorname{inv}_1,\dots,\operatorname{inv}_m$ of Galois extensions of number fields with a fixed Galois group. Then, we propose a heuristic in the spirit of Malle's conjecture which asymptotically predicts the number of extensions that satisfy $\operatorname{inv}_i\leq X_i$ for all $X_i$. The resulting conjecture is proved for abelian Galois groups. We also describe refined Artin conductors that carry essentially the same information as the invariants $\operatorname{inv}_1,\dots,\operatorname{inv}_m$.

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Fabian Gundlach. 2022-11-30. Malle's conjecture with multiple invariants. https://arxiv.org/abs/2211.16698

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