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→Examples: the Jacobi symbol and the Legendre symbol. |
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===Dirichlet series===
The L-function of completely (or totally) [[multiplicative function|multiplicative]] [[Dirichlet series]] <math>a(n)</math> satisfies
:<math>L(s,a)=\sum^\infty_{n=1}\frac{a(n)}{n^s}=\prod_p\biggl(1-\frac{a(p)}{p^s}\biggr)^{-1},</math>
which means that the sum all over the natural numbers is equal to the product all over the prime numbers.
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