  We give a criterion of integrality of an one-dimensional formal group law in
terms of congruences satisfied by the coefficients of the canonical invariant
differential. For an integral formal group law a p-adic analytic formula for
the local characteristic polynomial at p is given. We demonstrate applications
of our results to formal group laws attached to L-functions, Artin--Mazur
formal groups of algebraic varieties and hypergeometric formal group laws.
(This is the final version submitted to a journal; new parts are added in the
section on hypergeometric formal group laws.)

Number Theory