Kronecker symbol
The Kronecker symbol is a generalization of the Jacobi symbol to all integers.
Let be an integer, with prime factorization , where is a unit and the are primes. Let be an integer. The Kronecker symbol is defined to be
For odd , the number is simply the usual Legendre symbol. This leaves the case when . We define by
Since it extends the Jacobi symbol, the quantity is simply 1 when . When , we define it by
These extensions suffice to define the Kronecker symbol for all integer values .
Title | Kronecker symbol |
---|---|
Canonical name | KroneckerSymbol |
Date of creation | 2013-03-22 14:33:21 |
Last modified on | 2013-03-22 14:33:21 |
Owner | mathwizard (128) |
Last modified by | mathwizard (128) |
Numerical id | 6 |
Author | mathwizard (128) |
Entry type | Definition |
Classification | msc 11A07 |
Classification | msc 11A15 |
Synonym | Kronecker-Jacobi symbol |
Related topic | JacobiSymbol |
Related topic | LegendreSymbol |