Unit Reducible Fields and Perfect Unary Forms

Alar Leibak; Christian Porter; Cong Ling

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arXiv · 2207.06385

Unit Reducible Fields and Perfect Unary Forms

Alar Leibak·Christian Porter·Cong Ling

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Abstract

In this paper, we introduce the notion of unit reducibility for number fields, that is, number fields in which all positive unary forms attain their nonzero minimum at a unit. Furthermore, we investigate the link between unit reducibility and the number of homothety classes of perfect unary forms for a given number field, and prove an open conjecture about the number of classes of perfect unary forms in real quadratic fields, stated by D. Yasaki.

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Alar Leibak, Christian Porter, Cong Ling. 2022-07-13. Unit Reducible Fields and Perfect Unary Forms. https://arxiv.org/abs/2207.06385

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