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In number theory, a branch of mathematics, Ramanujan's ternary quadratic form is the algebraic expression x 2 + y 2 + 10z 2 with integral values for x, y and z. [ 1 ] [ 2 ] Srinivasa Ramanujan considered this expression in a footnote in a paper [ 3 ] published in 1916 and briefly discussed the representability of integers in this form.
This table collects 202 of the 331 invariants of ternary biquadratic forms. These forms are graded in two variables x and u . The horizontal direction of the table lists the invariants with increasing grades in x , while the vertical direction lists them with increasing grades in u .
A mapping q : M → R : v ↦ b(v, v) is the associated quadratic form of b, and B : M × M → R : (u, v) ↦ q(u + v) − q(u) − q(v) is the polar form of q. A quadratic form q : M → R may be characterized in the following equivalent ways: There exists an R-bilinear form b : M × M → R such that q(v) is the associated quadratic form.
Pages in category "Quadratic forms" ... Generalized Clifford algebra; Genus of a quadratic form; ... Ramanujan's ternary quadratic form; S. Signature (topology) ...
Use: {{Ternary|x}} where x is the decimal number. Example: {{Ternary|4632}} yields 20100120 3 . Numbers outside the range of -9007199254740992 to 9007199254740992 may lose precision.
The templates {} and {{EquationRef}} can be used to number equations. The template {{EquationNote}} can be used to refer to a numbered equation from surrounding text. For example, the following syntax: {{NumBlk |: |< math > x ^ 2 + y ^ 2 + z ^ 2 = 1 </ math >|{{EquationRef | 1}}}} produces the following result (note the equation number in the ...
A quadratic form with integer coefficients is called an integral binary quadratic form, often abbreviated to binary quadratic form. This article is entirely devoted to integral binary quadratic forms. This choice is motivated by their status as the driving force behind the development of algebraic number theory.
Gauss contributed to solving the Kepler conjecture in 1831 with the proof that a greatest packing density of spheres in the three-dimensional space is given when the centres of the spheres form a cubic face-centred arrangement, [127] when he reviewed a book of Ludwig August Seeber on the theory of reduction of positive ternary quadratic forms ...
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