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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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Montesinos Amilibia, José María (2015) On odd rank integral quadratic forms: canonical representatives of projective classes and explicit construction of integral classes with square-free determinant. Revista de la Real Academia de Ciencias Exactas Fisicas y Naturales Serie A: Matemáticas, 109 (1). pp. 199-245. ISSN 1578-7303

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Official URL: http://link.springer.com/article/10.1007/s13398-014-0176-4


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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.


Item Type:Article
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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]

Uncontrolled Keywords:Automorph; Commensurability class; Conway’s excesses; Hyperbolic manifold; Integral quadratic form; Orbifold; Projective equivalence; Rational equivalence
Subjects:Sciences > Mathematics
ID Code:30241
Deposited On:21 May 2015 10:15
Last Modified:12 Dec 2018 15:12

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