Fundamental Theorem of Genera

Consider h_+(d) proper equivalence classes of forms with discriminant d equal to the field discriminant, then they can be subdivided equally into 2^(r-1) genera of h_+(d)/2^(r-1) forms which form a subgroup of the proper equivalence class group under composition (Cohn 1980, p. 224), where r is the number of distinct prime divisors of d. This theorem was proved by Gauss in 1801.

See also

Form Genus, Genus Theorem

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Arno, S.; Robinson, M. L.; and Wheeler, F. S. "Imaginary Quadratic Fields with Small Odd Class Number.", H. Advanced Number Theory. New York: Dover, 1980.Gauss, C. F. Disquisitiones Arithmeticae. New Haven, CT: Yale University Press, 1966.

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Fundamental Theorem of Genera

Cite this as:

Weisstein, Eric W. "Fundamental Theorem of Genera." From MathWorld--A Wolfram Web Resource.

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