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arXiv · 2403.07171

Representing rational integers by generalized quadratic forms over quadratic fields

Ondřej Chwiedziuk·Matěj Doležálek·Emma Pěchoučková·Zdeněk Pezlar·Om Prakash·Giuliano Romeo·Anna Růžičková·Mikuláš Zindulka
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Abstract

We investigate generalized quadratic forms with values in the set of rational integers over quadratic fields. We characterize the real quadratic fields which admit a positive definite binary generalized form of this type representing every positive integer. We also show that there are only finitely many such fields where a ternary generalized form with these properties exists.

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Ondřej Chwiedziuk, Matěj Doležálek, Emma Pěchoučková, Zdeněk Pezlar, Om Prakash, Giuliano Romeo, Anna Růžičková, Mikuláš Zindulka. 2024-03-11. Representing rational integers by generalized quadratic forms over quadratic fields. https://arxiv.org/abs/2403.07171

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