Multivariate counting of wild abelian extensions
F. Gundlach, ArXiv:2607.27364 (2026).
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Let $K$ be a global function field of characteristic~$p$ and let $G$ be a finite abelian group of exponent $p^e$. We show that the multivariate generating function counting sub-$G$-extensions of $K$ with respect to $e$ specific height functions (encoding successive drops in the exponents of the higher ramification groups) is rational.
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arXiv:2607.27364
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Gundlach F. Multivariate counting of wild abelian extensions. arXiv:260727364. Published online 2026.
Gundlach, F. (2026). Multivariate counting of wild abelian extensions. In arXiv:2607.27364.
@article{Gundlach_2026, title={Multivariate counting of wild abelian extensions}, journal={arXiv:2607.27364}, author={Gundlach, Fabian}, year={2026} }
Gundlach, Fabian. “Multivariate Counting of Wild Abelian Extensions.” ArXiv:2607.27364, 2026.
F. Gundlach, “Multivariate counting of wild abelian extensions,” arXiv:2607.27364. 2026.
Gundlach, Fabian. “Multivariate Counting of Wild Abelian Extensions.” ArXiv:2607.27364, 2026.
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