Representing rational integers by generalized quadratic forms over quadratic fields

2024/03/11 by Chwiedziuk, Ondřej, Doležálek, Matěj, Pěchoučková, Emma +5
#11E20 #11E25 #11E39 #11R11 #11R80 #FOS: Mathematics #Number Theory (math.NT) #Primary 11E12 Secondary 11E16

paper · doi:10.48550/arxiv.2403.07171

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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