In mathematics, the Hilbert symbol or norm-residue symbol is a function (–, –) from K× × K× to the group of nth roots of unity in a local field K such...

lines. Use of arrow symbols in mathematical notation is still younger and developed in the first half of the 20th century. David Hilbert in 1922 introduced...

Hilbert ring Hilbert–Poincaré series Hilbert series and Hilbert polynomial Hilbert space Hilbert spectrum Hilbert system Hilbert transform Hilbert's arithmetic...

introduction of several other "symbols" used in algebraic number theory, such as the Hilbert symbol and the Artin symbol. Let p {\displaystyle p} be an...

\left({\tfrac {p}{q}}\right)=-1.} but he couldn't prove that either. Hilbert symbol (below) discusses how techniques based on the existence of solutions...

Carmichael lambda function of n). The n-th power residue symbol is related to the Hilbert symbol ( ⋅ , ⋅ ) p {\displaystyle (\cdot ,\cdot )_{\mathfrak {p}}}...

Hilbert symbol of a local field. The name "explicit reciprocity law" refers to the fact that the Hilbert symbols of local fields appear in Hilbert's reciprocity...

the symbol is sometimes called a Chevalley symbol or Artin–Chevalley symbol. The local Hilbert symbol of K can be written in terms of the Artin symbol for...

space Hilbert spectrum Hilbert symbol Hilbert system Hilbert transform Hilbert spectroscopy Hilbert–Huang transform Hilbert spectral analysis Hilbert-style...

{4}}} , in which case we can take n = | a | {\displaystyle n=|a|} . Hilbert symbol Kronecker, L. (1885), "Zur Theorie der elliptischen Funktionen", Sitzungsberichte...

In mathematics a Steinberg symbol is a pairing function which generalises the Hilbert symbol and plays a role in the algebraic K-theory of fields. It...

between (p/q) and (q/p). Hilbert reformulated the reciprocity laws as saying that a product over p of Hilbert norm residue symbols (a,b/p), taking values...

see e.g. Ch. IV of. Using the local reciprocity map, one defines the Hilbert symbol and its generalizations. Finding explicit formulas for it is one of...

"Hilbert-symbol equivalence of number fields". Tatra Mt. Math. Publ. 11: 7–16. Zbl 0978.11012. Czogała, A. (1999). "Higher degree tame Hilbert-symbol equivalence...

number field F, the group K2(F) is related to class field theory, the Hilbert symbol, and the solvability of quadratic equations over completions. In contrast...

and his own contribution lives on in the names of the Hilbert class field and of the Hilbert symbol of local class field theory. Results were mostly proved...

Vostokov developed an important class of explicit formulas for the Hilbert symbol on local fields, which have a wide range of applications in number theory...

Hilbert's biographer Constance Reid): "Through a proof of existence, Hilbert had been able to obtain a construction"; "the proof" (i.e. the symbols on...

especially mathematical logic, an axiomatic system, sometimes called a "Hilbert-style" deductive system, is a type of system of formal deduction developed...

local field, the Hasse invariant may be defined using the Hilbert symbol, the unique symbol taking values in C2. The invariants of a quadratic forms over...

groups. 1897 Hilbert publishes his Zahlbericht. 1897 Hilbert rewrites the law of quadratic reciprocity as a product formula for the Hilbert symbol. 1897 Kurt...

mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity...

Hilbert's axioms are a set of 20 assumptions proposed by David Hilbert in 1899 in his book Grundlagen der Geometrie (tr. The Foundations of Geometry) as...

In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent...

CITEREFRost1986 (help). The name "norm residue" originally referred to the Hilbert symbol ( a 1 , a 2 ) {\displaystyle (a_{1},a_{2})} , which takes values in...

construction Quotient ring construction Ward's twistor construction Hilbert symbol Hilbert's arithmetic of ends Colombeau's construction Vector bundle Integral...

Eisenstein and Kummer to Hilbert's product formula for the norm symbol. Artin's result provided a partial solution to Hilbert's ninth problem. Let L / K...

construction of quaternion algebras can be viewed as the quadratic Hilbert symbol of local class field theory. It is a theorem of Frobenius that there...

mechanics, a quantum state is typically represented as an element of a complex Hilbert space, for example, the infinite-dimensional vector space of all possible...

theory (also called p-adic Hodge theory), explicit formulas for the Hilbert symbol in local class field theory, see e.g. A local field is sometimes called...