Publication: On odd rank integral quadratic forms: canonical representatives of projective classes and explicit construction of integral classes with square-free determinant
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Publication Date
2015-03
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Springer
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Abstract
Two rank n, integral quadratic forms f and g are said projectively equivalent if there exist nonzero rational numbers r and s such that rf and sg are rationally equivalent. Two odd dimensional, integral quadratic forms f and g are projectivelly equivalent if and only if their adjoints are rationally equivalent. We prove that a canonical representative of each projective class of forms of odd rank, exists and is unique up to genus (integral equivalence for indefinite forms). We give a useful characterization of this canonical representative. An explicit construction of integral classes with square-free determinant is given. As a consequence, two tables of ternary and quinary integral quadratic forms of index 1 and with square-free determinant are presented.
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Erratum to On odd rank integral quadratic forms: canonical representatives of projective classes and explicit construction of integral classes with square-free determinant[RACSAM, (2015), 109(199-245), DOI 10.1007/s13398-014-0176-4]