The construction of perfect and extreme forms I

E. Barnes

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The construction of perfect and extreme forms II

E. Barnes (1959)

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Voronoï ’s algorithm is a method for obtaining the complete list of perfect $n$ -dimensional quadratic forms. Its generalization to $G$ -forms has the advantage of running in a lower-dimensional space, and furnishes a finite, and complete, classification of $G$ -perfect forms ( $G$ is a finite subgroup of $G L (n, ℤ))$ . We study the standard, $φ (m)$ -dimensional irreducible representation of the cyclic group $C_{m}$ of order $m$ , and give the, often new, densest $G$ -forms. Perfect cyclotomic forms are completely classified...

The least common denominator of the coefficients of a perfect quadratic form

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