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FEWNOMIALS AND INTERSECTIONS OF LINES WITHREAL ANALYTIC SUBGROUPS IN Gnm

Published online by Cambridge University Press:  18 January 2002

PAULA B. COHEN
Affiliation:
School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, 08540 NJ, USA and UMR AGAT au CNRS, Mathématiques, Bât M2, UFR de Mathématiques, Villeneuve d’Ascq, 59655, France; Paula.Cohen@univ-lille1.fr
UMBERTO ZANNIER
Affiliation:
School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, 08540 NJ, USA and Istituto Universitario di Architettura, Dipartimento di Costruzione, dell'Architettura, Santa Croce 191, 30135 Venezia, Italy; zannier@dimi.uniud.it
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Abstract

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.

Type
NOTES AND PAPERS
Copyright
© The London Mathematical Society 2002

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