A zero lemma
In 1981 \textit{D. W.~Masser} [Invent. Math. {63}, 81-95 (1981; Zbl 0436.32005)] proved a zero estimate for exponential polynomials in several variables which had a number of applications to transcendental number theory. This estimate was refined by several authors; especially \textit{P.~Philippon} [Bull. Soc. Math. Fr. {114}, 355-383 (1986; Zbl 0617.14001); Errata et addenda, ibid. {115}, 397-398 (1987; Zbl 0634.14001); Rocky Mt. J. Math. 26, 1069-1088 (1996; Zbl 0893.11027)]. Here the author introduces a further improvement which sharpens Philippon's results. The refinement arises from the fact that in the proof, the conditions he checks are not the same for each step. The main condition is the same, but the other ones are essentially less restrictive. In another work the author uses his zero estimate to derive sharp linear independence measures for two logarithms of algebraic numbers.
scientific article; zbMATH DE number 1803921