Examples
If p is an odd prime number, then the function
- where is the Legendre symbol, is a primitive Dirichlet character modulo p.
More generally, if m is a positive odd number, the function
- where is the Jacobi symbol, is a Dirichlet character modulo m.
These are quadratic characters: in general, the primitive quadratic characters arise precisely from the Kronecker symbol.
Read more about this topic: Dirichlet Character
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)
“In the examples that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”
—Michel de Montaigne (1533–1592)