Form Genus

Consider the forms Q for which the generic characters chi_i(Q) are equal to some preassigned array of signs e_i=1 or -1,


subject to product_(i=1)^(r)e_i=1. There are 2^(r-1) possible arrays, where r is the number of distinct prime divisors of a field discriminant d, and the set of forms corresponding to each array is called a genus of forms. The forms for which all e_i=1 are called the principal genus of forms, and each genus is also a collection of proper equivalence classes (Cohn 1980, pp. 223-224).

See also

Equivalence Class, Fundamental Theorem of Genera, Generic Character

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Cohn, H. "Compositions, Order, and Genera." Ch. 8 in Advanced Number Theory. New York: Dover, pp. 212-230, 1980.

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Form Genus

Cite this as:

Weisstein, Eric W. "Form Genus." From MathWorld--A Wolfram Web Resource.

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