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Montesinos Amilibia, José María 2023-06-18T06:44:59Z 2023-06-18T06:44:59Z 2015-03 1578-7303 10.1007/s13398-014-0176-4 https://hdl.handle.net/20.500.14352/24019 http://link.springer.com/article/10.1007/s13398-014-0176-4 http://www.springer.com/ 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. eng restricted access On odd rank integral quadratic forms: canonical representatives of projective classes and explicit construction of integral classes with square-free determinant journal article