In mathematics, Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer solution to an equation...

geometry (Hasse principle), and to local zeta functions. Hasse was born in Kassel, Province of Hesse-Nassau, the son of Judge Paul Reinhard Hasse, also written...

solution is also a solution in all completions. The local-global principle or Hasse principle asserts that for quadratic equations, the converse holds, as...

Martin Kneser, Günter Harder and Vladimir Chernousov (1989) proved the Hasse principle: for a simply connected semisimple group G over k, the map H 1 ( k...

Hardy–Littlewood circle method. For example, the Hasse–Minkowski theorem says that the Hasse principle holds for quadric hypersurfaces over a number field...

theorems of Helmut Hasse that are sometimes called Hasse's theorem: Hasse norm theorem Hasse's theorem on elliptic curves Hasse–Arf theorem Hasse–Minkowski theorem...

the Hasse principle for quadratic forms. For polynomials of degree larger than 2 the Hasse principle isn't valid in general. The idea of the Hasse principle...

this is both needed and worthwhile." Helmut Hasse's local–global principle, also known as the Hasse principle, is the idea that one can find an integer...

The initial result of this type was Eisenstein's theorem. Hasse principle The Hasse principle states that solubility for a global field is the same as...

reductive groups. Kottwitz (1988) proved it for all groups satisfying the Hasse principle, which at the time was known for all groups without E8 factors. V....

{\displaystyle {\sqrt {3}},} centered at the origin. More generally, the Hasse principle allows deciding whether a homogeneous Diophantine equation of degree...

the Hasse principle, capable of yielding quantitative information. If d is fixed and k is small, other methods are required, and indeed the Hasse principle...

solutions) provides also sufficient conditions, one says that the Hasse principle holds: this is the best possible situation. It does for quadratic forms...

published his work in 1923 and 1924. See Hasse principle, Hasse–Minkowski theorem. The local-global principle says that a general result about a rational...

D., but joint work with Cassels produced numerical examples on the Hasse principle for cubic surfaces. He subsequently went into computer science. He...

The Hasse principle would predict that if X has a rational point over all completions Kv of K, then X has a K-rational point. The Hasse principle holds...

a variety X over a global field, which measures the failure of the Hasse principle for X. If the value of the obstruction is non-trivial, then X may have...

Idele group Idele class group Adelic algebraic group Global field Hasse principle Hasse–Minkowski theorem Galois module Galois cohomology Brauer group Class...

conjecture abc Conjecture Catalan's conjecture Pillai's conjecture Hasse principle Diophantine set Matiyasevich's theorem Hundred Fowls Problem 1729 Davenport–Schmidt...

_{i\in I}k.} Consequently, (αi)i∈I = (0)i∈I. QED. Covering system Hasse principle Residue number system Katz 1998, p. 197 Dence & Dence 1999, p. 156...

In mathematics, the Hasse–Witt matrix H of a non-singular algebraic curve C over a finite field F is the matrix of the Frobenius mapping (p-th power mapping...

mathematics professor". The Daily Illini. Retrieved 8 December 2021. "Hasse Principle – Numberphile". YouTube. 1 June 2016. Haran, Brady. "Tom Crawford on...

In order theory, a Hasse diagram (/ˈhæsə/; German: [ˈhasə]) is a type of mathematical diagram used to represent a finite partially ordered set, in the...

their reductions modulo some or all prime numbers. See, for example, Hasse principle. Many recent developments of algebraic geometry were motivated by the...

in algebraic geometry. His work has focused on rational points, the Hasse principle, the Manin obstruction, exponential sums, and error-correcting codes...

the role of the Brauer group in accounting for obstructions to the Hasse principle via Grothendieck's theory of global Azumaya algebras, setting off a...

Venkatesh, jointly with Jordan Ellenberg, made significant progress on the Hasse principle for integral representations of quadratic forms by quadratic forms...

analog communications channel. Named for Ralph Hartley (1888–1970). Hasse principle is the idea that one can find an integer solution to an equation by...

1931 The Albert–Brauer–Hasse–Noether theorem proves the Hasse principle for simple algebras over global fields. 1933 Hasse classifies simple algebras...

K-rational point. Thus, the group measures the extent to which the Hasse principle fails to hold for rational equations with coefficients in the field...