• A zero lemma

Treffer: A zero lemma

Title:
A zero lemma
Authors:
Gouillon, Nicolas
Publisher Information:
Académie des Sciences, Paris
Subject Terms:
Results involving abelian varieties, Zero sets of holomorphic functions of several complex variables, Relevant commutative algebra, Zero estimate, Transcendence (general theory), linear forms in logarithms, Group varieties, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry, Exponential and trigonometric functions, Linear forms in logarithms, Baker's method
Document Type:
Fachzeitschrift Article
File Description:
application/xml
DOI:
10.1016/s1631-073x(02)02422-6
Access URL:
https://zbmath.org/1803921
Accession Number:
edsair.c2b0b933574d..a5a16ff252abaa1afe14f8efbe7cc910
Database:
OpenAIRE

Weitere Informationen

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.