An extension of the Jacobi Symbol to all Integers. It can be computed using the
normal rules for the Jacobi Symbol

(1) |

plus additional rules for ,

(2) |

(3) |

(4) |

The Kronecker Symbol is a Real Character modulo , and is, in fact, essentially the only type of Real primitive character (Ayoub 1963).

**References**

Ayoub, R. G. *An Introduction to the Analytic Theory of Numbers.* Providence, RI: Amer. Math. Soc., 1963.

Cohn, H. *Advanced Number Theory.* New York: Dover, p. 35, 1980.

© 1996-9

1999-05-26