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Fewnomials and Intersections of Lines with Real Analytic Subgroups in G m n
Author(s) -
Cohen Paula B.,
Zannier Umberto
Publication year - 2002
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s002460930100858x
Subject(s) - mathematics , multiplicative function , dimension (graph theory) , algebraic number , class (philosophy) , multiplicative group , combinatorics , group (periodic table) , algebra over a field , discrete mathematics , pure mathematics , mathematical analysis , chemistry , organic chemistry , artificial intelligence , computer science
In this paper, the authors study intersections of a special class of curves with algebraic subgroups of the multiplicative group of complex dimension at least 2. They show how results of Khovanskii on fewnomials can be used to derive finiteness results and bounds for the degrees of algebraic points for such intersections from more general results on intersections of curves with non‐algebraic subgroups. They thereby generalise their earlier results, and recover in some cases, using different methods, more uniform bounds than those given in related work of Bombieri, Masser and Zannier. 2000 Mathematics Subject Classification 11J99, 26C10.