Open AccessMultiplicative properties of integral binary quadratic forms
Author(s) -
A. G. Earnest,
Robert W. Fitzgerald
Publication year - 2009
Publication title -
contemporary mathematics - american mathematical society
Language(s) - English
Resource type - Reports
SCImago Journal Rank - 0.106
H-Index - 12
eISSN - 1098-3627
pISSN - 0271-4132
DOI - 10.1090/conm/493/09661
Subject(s) - mathematics , multiplicative function , binary number , binary quadratic form , quadratic equation , pure mathematics , quadratic function , arithmetic , mathematical analysis , geometry
In this paper, the integral binary quadratic forms for which the set of represented values is closed under k-fold products, for even positive integers k, will be characterized. This property will be seen to distinguish the elements of odd order in the form class group of a fixed discriminant. Further, it will be shown that this closure under k-fold products can always be expressed by a klinear mapping from (Z2)k to Z2. In the case k = 2, this resolves a conjecture of Aicardi and Timorin.
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