WebJan 1, 1997 · Hilbert symbol equivalence of degree n between two global fields containing a primitive nth root of unity is an isomorphism between the groups of nth power classes of … Web1. The Hilbert symbol Let Ebe a local eld of characteristic 6= 2. For a;b2E , the Hilbert symbol is de ned as (a;b) E= (1 if z2 = ax2 + by2 admits a nontrivial solution 1 otherwise: …
Higher degree tame hilbert-symbol equivalence of number …
The Hilbert symbol was introduced by David Hilbert (1897, sections 64, 131, 1998, English translation) in his Zahlbericht, with the slight difference that he defined it for elements of global fields rather than for the larger local fields. The Hilbert symbol has been generalized to higher local fields. See more 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 as the fields of reals or p-adic numbers . It is related to reciprocity laws, … See more • Azumaya algebra See more • "Norm-residue symbol", Encyclopedia of Mathematics, EMS Press, 2001 [1994] • HilbertSymbol at Mathworld See more Over a local field K whose multiplicative group of non-zero elements is K , the quadratic Hilbert symbol is the function (–, –) from K × K to {−1,1} defined by Equivalently, See more If K is a local field containing the group of nth roots of unity for some positive integer n prime to the characteristic of K, then the Hilbert symbol (,) is a function from K*×K* to μn. In terms of … See more Webpdf, <1MB, bf02940871.pdf Higher degree tame hilbert-symbol equivalence of number fields Vandenhoeck & Ruprecht; Springer-Verlag; Springer Verlag; Springer Science and Business … inc blue
algebraic number theory - How to compute the Hilbert symbol ...
Web1 Answer Sorted by: 6 On Q p the Hilbert symbol ( a, b) depends only on the classes of a and b modulo ( Q p ×) 2. There are eight such classes when p = 2. So, if nothing better, you can … WebOct 23, 2024 · The Hilbert symbol was introduced by David Hilbert in his Zahlbericht (1897), with the slight difference that he defined it for elements of global fields rather than for the … WebFeb 9, 2024 · Hilbert symbol Let K K be any local field. For any two nonzero elements a,b ∈K× a, b ∈ K ×, we define: (a,b):={+1 if z2 = ax2+by2 has a nonzero solution (x,y,z) ≠ (0,0,0) in K3, −1 otherwise. ( a, b) := { + 1 if z 2 = a x 2 + b y 2 has a nonzero solution ( x, y, z) ≠ ( 0, 0, 0) in K 3, - 1 otherwise. in between office i lose the will to work