Hatcher-Topology-of-Numbers · Problem 5.1.1

Classification of Quadratic Forms

Mathematics — Algebraic Topology · four-types-of-forms

Problem

(a) Find two primitive elliptic forms ax2+cy2ax^2 + cy^2 that have the same discriminant but take on different sets of values. Draw enough of the topographs of the two forms to make it apparent that they do not have exactly the same sets of values. (Remember that the topograph only shows the values Q(x,y)Q(x,y) for primitive pairs (x,y)(x,y).) (b) Do the same thing with hyperbolic forms ax2+cy2ax^2 + cy^2.

Related theory

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