On the number of zeros of exponential polynomials and related questions

Abstract

We apply Straßmann's theorem to p–adic power series satisfying linear differential equations with polynomial coefficients and note that our approach leads to our estimating the number of integer zeros of polynomials on a given interval and thence to an investigation of the number of p–adic small values of a function on such an interval, that is, of the number of solutions of a congruence modulo pr.