Representing rational integers by generalized quadratic forms over quadratic fields

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.

16 pages + 11 pages appendix; moved technical details to the appendix