Universal quadratic forms and Dedekind zeta functions

Vítězslav Kala; Mentzelos Melistas

doi:10.48550/arXiv.2311.12911

Universal quadratic forms and Dedekind zeta functions

Vítězslav Kala
, Mentzelos Melistas

Mathematics of Operations Research

Research output: Working paper › Preprint › Academic

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Abstract

We study universal quadratic forms over totally real number fields using Dedekind zeta functions. In particular, we prove an explicit upper bound for the rank of universal quadratic forms over a given number field $K$, under the assumption that the codifferent of $K$ is generated by a totally positive element. Motivated by a possible path to remove that assumption, we also investigate the smallest number of generators for the positive part of ideals in totally real numbers fields.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2311.12911
Publication status	Published - 21 Nov 2023

Keywords

math.NT
11E12, 11E20, 11H06

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10.48550/arXiv.2311.12911

ArticleSubmitted version, 223 KB

Universal quadratic forms and Dedekind zeta functions
Kala, V. & Melistas, M., Aug 2024, In: International Journal of Number Theory. 20, 7, p. 1833–1847 15 p.
Research output: Contribution to journal › Article › Academic › peer-review
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Universal quadratic forms and Dedekind zeta functions

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Universal quadratic forms and Dedekind zeta functions

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