A Note on Maurin’s Theorem

Enrico Bombieri, Philipp Habegger, David Masser, Umberto Zannier

Type: Article

Publication Date: 2010-07-25

Citations: 12

DOI: https://doi.org/10.4171/rlm/570

Abstract

We combine the strategy described in a paper of the first, third and fourth authors with a recent result of the second author to obtain a new proof of Maurin’s Theorem to the effect that the points satisfying two independent multiplicative relations on a fixed algebraic curve form a finite set when there is no natural obstacle.

Locations

Rendiconti Lincei Matematica e Applicazioni - View - PDF

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Works That Cite This (12)

Action	Title	Year	Authors
+	Equations multiplicatives sur les sous-varietes des tores	2011	Guillaume Maurin
+ PDF Chat	On the Győry-Sárközy-Stewart conjecture in function fields	2018	Igor E. Shparlinski
+	Unlikely intersections for curves in additive groups over positive characteristic	2016	W. Dale Brownawell David Masser
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+ PDF Chat	Rational points on Grassmannians and unlikely intersections in tori	2016	Laura Capuano David Masser Jonathan Pila Umberto Zannier
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+	Functional transcendence via o-minimality	2015	Jonathan Pila
+ PDF Chat	On elements of large order on elliptic curves and multiplicative dependent images of rational functions over finite fields	2021	Bryce Kerr Jorge Mello Igor E. Shparlinski
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Works Cited by This (11)

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+	Heights in Diophantine geometry	2006	Enrico Bombieri Walter Gubler
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+	Courbes algébriques et équations multiplicatives	2008	Guillaume Maurin
+ PDF Chat	On the Bounded Height Conjecture	2008	Philipp Habegger
+ PDF Chat	Finiteness results for multiplicatively dependent points on complex curves	2003	Enrico Bombieri David Masser Umberto Zannier
+ PDF Chat	On unlikely intersections of complex varieties with tori	2008	Enrico Bombieri David Masser Umberto Zannier
+	EXPONENTIAL SUMS EQUATIONS AND THE SCHANUEL CONJECTURE	2002	Boris Zilber
+	Anomalous Subvarieties—Structure Theorems and Applications	2007	Enrico Bombieri David Masser Umberto Zannier
+	Le problème de Lehmer en dimension supérieure	1999	Francesco Amoroso S. David
+	A relative Dobrowolski lower bound over abelian extensions	2000	Francesco Amoroso Umberto Zannier