transfinite arithmetic, cardinal arithmetic, ordinal arithmetic
prime field, p-adic integer, p-adic rational number, p-adic complex number
arithmetic geometry, function field analogy
symmetric monoidal (∞,1)-category of spectra
The rational zero theorem or rational root theorem states:
Given a natural number and a degree polynomial function on the rational numbers with integers valued coefficients and , defined as
then the fiber of at is inhabited if one of the following is true:
,
and there exists integers and such that , , and .
The rational root theorem for polynomials states:
Given a natural number and a degree univariate polynomial on the rational numbers where , there exists a degree univariate polynomial where such that if and only if there exists an integer such that and .
Last revised on June 17, 2022 at 17:20:05. See the history of this page for a list of all contributions to it.