The set of solutions of a polynomial-exponential equation
Scott Ahlgren · Acta Arithmetica · 1999
l∈λ Pl(x)αl = 0 (λ ∈ P). Denote by S(P) the set of solutions of (1.1)P which do not satisfy (1.1)Q for any proper refinement Q of P (notice that every solution of (1.1) lies in S(P) for some partition P). Then let G(P) be the subgroup of Z consisting of x such that αl = α x m whenever l and m lie in the same set λ of P. Let d be the degree of the field K, and for l ∈ Λ let δl be the total degree of the polynomial Pl. Set