A report on Binary quadratic form
Quadratic homogeneous polynomial in two variables
- Binary quadratic form6 related topics with Alpha
Bhargava cube
0 linksConfiguration consisting of eight integers placed at the eight corners of a cube.
Configuration consisting of eight integers placed at the eight corners of a cube.
To each pair of opposite faces of a Bhargava cube one can associate an integer binary quadratic form thus getting three binary quadratic forms corresponding to the three pairs of opposite faces of the Bhargava cube.
Genus of a quadratic form
0 linksClassification of quadratic forms and lattices over the ring of integers.
Classification of quadratic forms and lattices over the ring of integers.
For binary quadratic forms there is a group structure on the set C of equivalence classes of forms with given discriminant.
Fermat's theorem on sums of two squares
0 linksOdd prime p can be expressed as:
Odd prime p can be expressed as:
An (integral binary) quadratic form is an expression of the form, as required.
Manjul Bhargava
0 linksCanadian-American mathematician.
Canadian-American mathematician.
His PhD thesis generalized Gauss's classical law for composition of binary quadratic forms to many other situations.
Infrastructure (number theory)
0 linksInfrastructure is a group-like structure appearing in global fields.
Infrastructure is a group-like structure appearing in global fields.
D. Shanks observed the infrastructure in real quadratic number fields when he was looking at cycles of reduced binary quadratic forms.
Ideal class group
0 linksAlgebraic number field
Algebraic number field
For d < 0, the ideal class group of Q(√d) is isomorphic to the class group of integral binary quadratic forms of discriminant equal to the discriminant of Q(√d).