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- W1493445793 abstract "We introduce two notions of equivalence for rational quadratic forms. Two $n$-ary rational quadratic forms are commensurable if they possess commensurable groups of automorphisms up to isometry. Two $n$-ary rational quadratic forms $F$ and $G$ are projectivelly equivalent if there are nonzero rational numbers $r$ and $s$ such that $rF$ and $sG$ are rationally equivalent. It is shown that if $F$ and $G$ have Sylvester signature ${-,+,+,...,+}$ then $F$ and $G$ are commensurable if and only if they are projectivelly equivalent. The main objective of this paper is to obtain a complete system of (computable) numerical invariants of rational $n$-ary quadratic forms up to projective equivalence. These invariants are a variation of Conway's $p$-excesses. Here the cases $n$ odd and $n$ even are surprisingly different. The paper ends with some examples" @default.
- W1493445793 created "2016-06-24" @default.
- W1493445793 creator A5039042538 @default.
- W1493445793 date "2013-11-01" @default.
- W1493445793 modified "2023-10-17" @default.
- W1493445793 title "On integral quadratic forms having commensurable groups of automorphisms" @default.
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- W1493445793 doi "https://doi.org/10.32917/hmj/1389102581" @default.
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