The Jacobi symbol is a generalization of the Legendre symbol. Introduced by Jacobi in 1837, it is of theoretical interest in modular arithmetic and other...
45 KB (2,356 words) - 04:14, 3 October 2024
symbol, written as ( a n ) {\displaystyle \left({\frac {a}{n}}\right)} or ( a | n ) {\displaystyle (a|n)} , is a generalization of the Jacobi symbol to...
13 KB (1,722 words) - 12:00, 5 February 2024
Carl Gustav Jacob Jacobi (/dʒəˈkoʊbi/; German: [jaˈkoːbi]; 10 December 1804 – 18 February 1851) was a German mathematician who made fundamental contributions...
20 KB (2,058 words) - 09:02, 13 September 2024
Generalizations of the symbol include the Jacobi symbol and Dirichlet characters of higher order. The notational convenience of the Legendre symbol inspired introduction...
43 KB (2,394 words) - 11:51, 27 July 2024
doubly-periodic functions Jacobi polynomials, a class of orthogonal polynomials Jacobi symbol, a generalization of the Legendre symbol Jacobi coordinates, a simplification...
1 KB (201 words) - 12:46, 4 November 2022
it is 0 if p divides a. The same notation is used for the Jacobi symbol and Kronecker symbol, which are generalizations where p is respectively any odd...
74 KB (9,776 words) - 16:31, 14 October 2024
Quadratic reciprocity (section Jacobi symbol)
function and a certain Dirichlet L-function The Jacobi symbol is a generalization of the Legendre symbol; the main difference is that the bottom number...
111 KB (8,556 words) - 14:19, 23 September 2024
and let ( D n ) {\displaystyle \left({\tfrac {D}{n}}\right)} be the Jacobi symbol. We define δ ( n ) = n − ( D n ) . {\displaystyle \delta (n)=n-\left({\tfrac...
25 KB (3,643 words) - 07:05, 26 November 2023
Zolotarev's lemma (section Jacobi symbol)
and p. This interpretation of the Legendre symbol as the sign of a permutation can be extended to the Jacobi symbol ( a n ) , {\displaystyle \left({\frac {a}{n}}\right)...
6 KB (793 words) - 08:11, 2 September 2021
{a}{n}}\right)} is the Jacobi symbol. If n is an odd composite integer that satisfies the above congruence, then n is called an Euler–Jacobi pseudoprime (or...
3 KB (358 words) - 22:23, 11 January 2024