TOPICS
Search

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,

 e_1,e_2,...,e_r,

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

Explore with Wolfram|Alpha

WolframAlpha

More things to try:

References

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

Referenced on Wolfram|Alpha

Form Genus

Cite this as:

Weisstein, Eric W. "Form Genus." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FormGenus.html

Subject classifications