Solving integer equations from all modular solutions
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 by using the Chinese remainder theorem to piece together solutions modulo powers of each different prime number. This is handled by examining the equation in the completions of the rational numbers: the real numbers and the p-adic numbers. A more formal version of the Hasse principle states that certain types of equations have a rational solution if and only if they have a solution in the real numbers and in the p-adic numbers for each prime p.
In mathematics, Helmut Hasse's local–global principle, also known as the Hasseprinciple, is the idea that one can find an integer solution to an equation...
solution is also a solution in all completions. The local-global principle or Hasseprinciple asserts that for quadratic equations, the converse holds, as...
geometry (Hasseprinciple), and to local zeta functions. Hasse was born in Kassel, Province of Hesse-Nassau, the son of Judge Paul Reinhard Hasse, also written...
Martin Kneser, Günter Harder and Vladimir Chernousov (1989) proved the Hasseprinciple: 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 Hasseprinciple holds for quadric hypersurfaces over a number field...
The initial result of this type was Eisenstein's theorem. Hasseprinciple The Hasseprinciple states that solubility for a global field is the same as...
the Hasseprinciple for quadratic forms. For polynomials of degree larger than 2 the Hasseprinciple isn't valid in general. The idea of the Hasse principle...
{\displaystyle {\sqrt {3}},} centered at the origin. More generally, the Hasseprinciple allows deciding whether a homogeneous Diophantine equation of degree...
D., but joint work with Cassels produced numerical examples on the Hasseprinciple for cubic surfaces. He subsequently went into computer science. He...
The Hasseprinciple would predict that if X has a rational point over all completions Kv of K, then X has a K-rational point. The Hasseprinciple holds...
1931 The Albert–Brauer–Hasse–Noether theorem proves the Hasseprinciple for simple algebras over global fields. 1933 Hasse classifies simple algebras...
a variety X over a global field, which measures the failure of the Hasseprinciple for X. If the value of the obstruction is non-trivial, then X may have...
Venkatesh, jointly with Jordan Ellenberg, made significant progress on the Hasseprinciple for integral representations of quadratic forms by quadratic forms...
solutions) provides also sufficient conditions, one says that the Hasseprinciple holds: this is the best possible situation. It does for quadratic forms...
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...
2001 - Elsevier doi:10.1006/jabr.2001.8830 Classical groups and the Hasseprinciple, E Bayer-Fluckiger, R Parimala - Annals of Mathematics, 1998 - jstor...
their reductions modulo some or all prime numbers. See, for example, Hasseprinciple. Many recent developments of algebraic geometry were motivated by the...
the role of the Brauer group in accounting for obstructions to the Hasseprinciple via Grothendieck's theory of global Azumaya algebras, setting off a...
analog communications channel. Named for Ralph Hartley (1888–1970). Hasseprinciple is the idea that one can find an integer solution to an equation by...
in algebraic geometry. His work has focused on rational points, the Hasseprinciple, the Manin obstruction, exponential sums, and error-correcting codes...
Founding Fellow of the Learned Society of Wales. He showed that the Hasseprinciple holds for non-singular cubic forms in at least nine variables. Prof...
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