mathematics, the Hasse invariant (or Hasse–Witt invariant) of a quadratic form Q over a field K takes values in the Brauer group Br(K). The name "Hasse–Witt" comes...

mathematics, Hasse invariant may refer to: Hasse invariant of an algebra Hasse invariant of an elliptic curve Hasse invariant of a quadratic form This disambiguation...

In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). For example, 4 x...

The Hasse–Minkowski theorem is a fundamental result in number theory which states that two quadratic forms over a number field are equivalent if and only...

1923 Hasse diagram Hasse invariant of an algebra Hasse invariant of an elliptic curve Hasse invariant of a quadratic form Artin–Hasse exponential Hasse–Weil...

October 1910 – 26 December 1997) was a Turkish mathematician. He is known for the Arf invariant of a quadratic form in characteristic 2 (applied in knot...

well-defined. The Hasse invariant of a quadratic form is again a well-defined function on Witt classes with values in the Brauer group of the field of definition...

a finite basis (with one element) for the invariants of binary quadratic forms. Noether's advisor, Paul Gordan, was known as the "king of invariant theory"...

Multiplicative order Discrete logarithm Quadratic residue Euler's criterion Legendre symbol Gauss's lemma (number theory) Congruence of squares Luhn formula Mod n...

theory, particularly for the theory of automorphic representations, and the arithmetic of quadratic forms. In case G is a linear algebraic group, it is an...

Stiefel–Whitney classes for quadratic forms over fields, the first two cases being the discriminant and the Hasse–Witt invariant (Milnor 1970). For a real vector bundle...

group then the corresponding invariant is essentially the Hasse−Witt invariant. If G is the orthogonal group of a quadratic form in characteristic not 2,...

defined for a binary quadratic form. It is a special case of a Hasse–Weil L-function. The natural definition of L(E, s) only converges for values of s in the...

injectivity of the left arrow is the content of the Albert–Brauer–Hasse–Noether theorem. The fact that the sum of all local invariants of a central simple...

Albert–Brauer–Hasse–Noether theorem, saying that a central simple algebra over a number field is determined by its local invariants. Building on the Hasse principle...

the j-invariant of the curve lies in a quadratic extension of the prime field of K, a finite field of order p2. Suppose E is in Legendre form, defined...

The canonical height on an abelian variety is a height function that is a distinguished quadratic form. See Néron–Tate height. Chabauty's method Chabauty's...

(number theory) Sylvester pentahedral theorem (invariant theory) Sylvester's law of inertia (quadratic forms) Sylvester–Gallai theorem (plane geometry) Symmetric...

{1}{2}}\\\end{bmatrix}}} The Hasse diagram for the F4 root poset is shown below right. Just as O(n) is the group of automorphisms which keep the quadratic polynomials...

important ingredient is a function of a complex variable, L, the Hasse–Weil zeta function of E over Q. This function is a variant of the Riemann zeta function...

value of the Arf invariant of a certain quadratic form Q with values mod 2. Thus in case of g = 3 and a plane quartic curve, there were 28 of one type...

classical law for composition of binary quadratic forms to many other situations. One major use of his results is the parametrization of quartic and quintic orders...

arithmetic of quadratic forms, especially concerning n variables, and his research into that topic led him to consider certain geometric properties in a space...

original quadratic reciprocity law can be hard to see. The class number formula relates many important invariants of a number field to a special value of its...

local–global principle. For example, the Hasse–Minkowski theorem reduces the problem of finding rational solutions of quadratic equations to solving these equations...

a group and showing its size is such that p {\displaystyle p} is prime. For ECPP the group is an elliptic curve over a finite set of quadratic forms such...

n-dimensional Lie algebra over the ring R, defined in terms of the quadratic part F2 of the formal group law. [x,y] = F2(x,y) − F2(y,x) The natural functor...

make use of the fact that groups of the form E ( F q ) {\displaystyle E(\mathbb {F} _{q})} are subject to an important theorem due to Hasse, that bounds...

{\displaystyle d} , the quadratic field Q ( d ) {\displaystyle \mathbb {Q} ({\sqrt {d}})} is a number field obtained by adjoining the square root of d {\displaystyle...

range of fundamental ideas including invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry...