Additive polynomial

In mathematics, an additive polynomial is the basic object of study classical algebraic number theory.

Let k be a field of finite characteristic p. Let $P(x)\in k[x]$ be a polynomial in x with coefficients in k. Such a polynomial $P(x)$ is called additive if and only if $P(a+b)=P(a)+P(b)\mod p$ for $a,b,a+b\in k$.

References

• David Goss, Basic Structures of Function Field Arithmetic, 1996, Springer, Berlin.