Papers › Representing rational integers by generalized quadratic forms over quadratic fields
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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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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