Binary quadratic form: Difference between revisions

Revision as of 18:54, 5 February 2023

Revision as of 07:56, 22 December 2023

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Another instance of quadratic forms is [[Pell's equation]] <math>x^2-ny^2=1</math>.

Binary quadratic forms are closely related to ideals in quadratic fields,. thisThis allows the class number of a quadratic field to be calculated by counting the number of reduced binary quadratic forms of a given discriminant.

The classical theta function of 2 variables is <math> \sum_{(m,n)\in \mathbb{Z}^2} q^{m^2 + n^2}</math>, if <math>f(x,y)</math> is a positive definite quadratic form then <math> \sum_{(m,n)\in \mathbb{Z}^2} q^{f(m,n)}</math> is a theta function.