arXiv subjects

Ondřej Chwiedziuk

Publications and source records attributed to Ondřej Chwiedziuk.

2 recordsLinked to original sources

arXiv2026

Representing rational integers by generalized quadratic forms over quadratic fields

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.

math.NT↗

arXiv2024

No proper generalized quadratic forms are universal over quadratic fields

We consider generalized quadratic forms over real quadratic number fields and prove, under a natural positive-definiteness condition, that a generalized quadratic form can only be universal if it contains a quadratic subform that is universal. We also construct an example illustrating that the positive-definiteness condition is necessary.

math.NT↗