AMEDEO SCREMIN
Exponential Diophantine equations and inequalities
Pages: 301-309
Received: 29 February 2004
Mathematics Subject Classification (2000): 11D45 - 11D61
Abstract: Let us consider the ring of power sums with algebraic coefficients and positive integral roots, i.e. of functions of N of the form
(1) a(n) = b1cn 1 + b2cn 2 + ... + bhcn h,
with biÎ
(2) a0(n)yd + a1(n)yd-1 + ... + a d-1(n)y + ad(n) = 0
and the inequality
(3) |F(n,y)|< a(n-d-1-e),
where a0, ..., ad are power sums, e > 0, F is monic in y and a is a quantity depending on the dominant roots of the power sums appearing as coefficients in F. We will show that, under suitable assumptions, for all the solutions of (2), y can be parametrized by some power sum in a finite set. We will reach a similar conclusion also for (3).