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Representation of spinor exceptional integers by ternary quadratic forms

Published online by Cambridge University Press:  22 January 2016

A. G. Earnest
A. G. Earnest*
Affiliation:
Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901, USA
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The existence and basic properties of what are now referred to as spinor exceptional integers for a genus of integral ternary quadratic forms were first observed in the 1950’s by Jones and Watson [7] and Kneser [8] in the context of indefinite forms. The study of these integers and their generalizations has been undertaken by a number of authors in recent years, and has contributed significantly to the understanding of representation properties unique to ternary forms. In this direction, the present author proved in a previous paper [4] that if c is a primitive spinor exceptional integer for a genus of integral ternary quadratic forms and f is some form in this genus, then a form in the spinor genus of f primitively represents c if and only if f primitively represents an integer of the type ct2, for some odd positive integer t, relatively prime to the discriminant d, which satisfies the condition that the Jacobi symbol (–cd/t) equals 1.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 93 , March 1984 , pp. 27 - 38
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1984

References

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