Newton-Hensel Interpolation Lifting

The main result of this paper is a new version of Newton-Hensel lifting that relates to interpolation questions. It allows one to lift polynomials in Z[x] from information modulo a prime number p 6= 2 to a power pk for any k , and its originality is that it is a mixed version that not only lifts the coefficients of the polynomial but also its exponents. We show that this result corresponds exactly to a Newton-Hensel lifting of a system of 2t generalized equations in 2t unknowns in the ring of p -adic integers Zp . Finally we apply our results to sparse polynomial interpolation in Z[x] .