Abstract
The seminal papers in the field of root-discriminant bounds are those of Odlyzko and Martinet. Both papers include the question of whether the field \(\mathbb {Q}(\sqrt{-5460})\) has finite or infinite 2-class tower. This is a critical case that will either substantially lower the best known upper bound for lim inf of root discriminants (if infinite) or else give a counter-example to what is often termed Martinet’s conjecture or question (if finite). Using extensive computation and introducing some new techniques, we give strong evidence that the tower is in fact finite, establishing other properties of its Galois group en route.
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Acknowledgements
The authors thank Charles Leedham-Green for his comments on the paper. The first author was supported by Simons Foundation Award MSN-179747. The second author was supported by National Science Foundation grant DMS-1301690.
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Boston, N., Wang, J. (2018). The 2-Class Tower of \(\mathbb {Q}(\sqrt{-5460})\). In: Akbary, A., Gun, S. (eds) Geometry, Algebra, Number Theory, and Their Information Technology Applications. GANITA 2016. Springer Proceedings in Mathematics & Statistics, vol 251. Springer, Cham. https://doi.org/10.1007/978-3-319-97379-1_5
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