In number theory, Hilbert's irreducibility theorem, conceived by David Hilbert in 1892, states that every finite set of irreducible polynomials in a finite...

is finitely generated Hilbert's irreducibility theorem, in number theory, concerning irreducible polynomials Hilbert's Nullstellensatz, the basis of algebraic...

In mathematics, Hilbert's Nullstellensatz (German for "theorem of zeros", or more literally, "zero-locus-theorem") is a theorem that establishes a fundamental...

ends Hilbert's paradox of the Grand Hotel Hilbert–Schmidt operator Hilbert–Smith conjecture Hilbert–Burch theorem Hilbert's irreducibility theorem Hilbert's...

rational functions in an indeterminate t. After that, one applies Hilbert's irreducibility theorem to specialise t, in such a way as to preserve the Galois group...

sum of irreducible finite-dimensional unitary representations of G. To state the third and final part of the theorem, there is a natural Hilbert space...

theorem (number theory) Hilbert's irreducibility theorem (number theory) Hurwitz's theorem (number theory) Jacobi's four-square theorem (number theory) Jurkat–Richert...

("Hilbertian field" being defined here as a field for which Hilbert's Irreducibility Theorem holds, such as the rational numbers and function fields.) Ax...

which has come to be known as the Riemann–Hilbert problem. Hilbert's work was mainly concerned with the Hilbert transform for functions defined on the circle...

criterion Perron's irreducibility criterion Hilbert's irreducibility theorem Cohn's irreducibility criterion Irreducible component of a topological space Factorization...

Gelfand–Naimark theorem states that an arbitrary C*-algebra A is isometrically *-isomorphic to a C*-subalgebra of bounded operators on a Hilbert space. This...

In matrix theory, the Perron–Frobenius theorem, proved by Oskar Perron (1907) and Georg Frobenius (1912), asserts that a real square matrix with positive...

In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential can be expressed as plane waves...

Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states the following: Lindemann–Weierstrass theorem—if α1...

implies the corresponding Stone–von Neumann theorem for Heisenberg groups Hn(Z/pZ), particularly: Irreducibility of Uh Pairwise inequivalence of all the representations...

Bézout's theorem is a statement concerning the number of common zeros of n polynomials in n indeterminates. In its original form the theorem states that...

versions of the Mordell–Weil theorem, Thue–Siegel–Roth theorem, Siegel's theorem, with a treatment of Hilbert's irreducibility theorem and applications (in the...

elements are irreducible. The converse does not hold in general, but does hold for unique factorization domains. The fundamental theorem of arithmetic...

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension...

structure as Hilbert space operators. The Peter–Weyl theorem holds, and a version of the Fourier inversion formula (Plancherel's theorem) follows: if...

{\displaystyle L^{2}} ). The theorem also holds in many non-abelian locally compact groups, except that the set of irreducible unitary representations G...

unitary representation on a Hilbert space V {\displaystyle V} is the direct sum of irreducible representations. Irreducible representations are always...

unitary equivalence classes of irreducible *-representations of A. A *-representation π of A on a Hilbert space H is irreducible if, and only if, there is...

which corresponds to a real eigenvalue. Theorem For every compact self-adjoint operator T on a real or complex Hilbert space H, there exists an orthonormal...

generalization of complete fields. Hilbertian field A field satisfying Hilbert's irreducibility theorem: formally, one for which the projective line is not thin in...

Although an isomorphism could always be found that maps one Hilbert space into the other, Haag's theorem implies that no such mapping could deliver unitarily...

representation of the fundamental group of the sphere punctured in two points. Hilbert's 21st problem asks whether every suitable monodromy representation arises...

definition. The rational number field Q is Hilbertian, because Hilbert's irreducibility theorem has as a corollary that the projective line over Q is Hilbertian:...

of Riesz's presentation of Hilbert's spectral theorems at the time, and the discovery of Hermitian operators in a Hilbert space, as distinct from self-adjoint...

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations...