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arXiv · 2404.12844

Failures of integral Springer's Theorem

Nicolas Daans·Vítězslav Kala·Jakub Krásenský·Pavlo Yatsyna
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Abstract

We discuss the phenomenon where an element in a number field is not integrally represented by a given positive definite quadratic form, but becomes integrally represented by this form over a totally real extension of odd degree. We prove that this phenomenon happens infinitely often, and, conversely, establish finiteness results about the situation when the quadratic form is fixed.

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Nicolas Daans, Vítězslav Kala, Jakub Krásenský, Pavlo Yatsyna. 2024-04-19. Failures of integral Springer's Theorem. https://doi.org/10.1090/proc/17141

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