Hilbert symbol information

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...

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...

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

\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...

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

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...

{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...

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...

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...

mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of formal...

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...

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...

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...

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...

corner has been used by Peirce. Implication: the symbol → {\displaystyle \to } appeared in Hilbert in 1918;: 76  ⊃ {\displaystyle \supset } was used...