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Near universal property of a quadratic form of Hessian discriminant 4


Jesse Ira Deutsch

Abstract

A quadratic form is universal if it represents all totally positive integers in a number field. In classical number theory over the rational  integers there are some results where a quadratic form takes on all positive integer values except for a certain restricted set. Here we  show that one of the quaternary quadratic forms proven universal for Q( √5) takes on all totally positive values in Q( √2) except for a certain infinite set. The exceptional integers have even norm and the highest power of 2 dividing that norm is 2 to the first power.


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eISSN: 1727-933X
print ISSN: 1607-3606