The connection between quadratic forms and the extended modular group

Abstract

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

n-Universal quadratic forms and quadratic forms over finite fields

“…(for further details on binary quadratic forms see [1,2,5,9]). Most properties of quadratic forms can be given with the aid of the extended modular group Γ (see [10]). Gauss defined the group action of Γ on the set of forms as follows: gF (x, y) = ar 2 + brs + cs 2 x 2 + (2art + bru + bts + 2csu) xy…”

On the Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms

“…There is a strong connection between the extended modular group and binary quadratic forms (for further details see [5]). Most properties of binary quadratic forms can be given by the aid of the extended modular group.…”