Counting problems and semisimple groups.
Voronoï ’s algorithm is a method for obtaining the complete list of perfect -dimensional quadratic forms. Its generalization to -forms has the advantage of running in a lower-dimensional space, and furnishes a finite, and complete, classification of -perfect forms ( is a finite subgroup of . We study the standard, -dimensional irreducible representation of the cyclic group of order , and give the, often new, densest -forms. Perfect cyclotomic forms are completely classified for and for...