Umberto Zannier - Selected publications#


Some Problems of Unlikely Intersections in Arithmetic and Geometry, Annals of Mathematics Studies, n. 181, Princeton University Press, 2012.
(BOOK, 160 pp.: introduces to the theory of Unlikely Intersections, both in tori and abelian varieties, and presents a recent method and some applications of it to conjectures of Pink and - by J. Pila - of the conjecture of André-Oort.)

Torsion anomalous points and families of elliptic curves.
Amer. J. Math. 132 (2010), no. 6, 1677–1691.
(Research paper, in coll. with D. Masser, introduces a new method and solves case of Pink's conjecture for families of abelian surfaces.)

Hilbert irreducibility above algebraic groups. Duke Math. J. 153 (2010), no. 2, 397-425.
(Research paper; proves Hilbert Irreducibility for lifting of points in cyclic groups in tori or powers of elliptic curves, and proves a Bertini's theorem for algebraic subgroups of tori.)

On composite lacunary polynomials and the proof of a conjecture of Schinzel , Inventiones Mathematicae, vol. 174 (2008), 127-138
(Research paper; solves completely a conjecture of P. Erdos and A. Schinzel concerning composite polynomials.)

Cyclotomic Diophantine Problems, Duke Mathematical Journal, No. 3 (2007), 527-554.
(Research paper, in coll. with R. Dvornicich; solves questions of W. Narkiewicz on arithmetic dynamics).

Anomalous subvarieties-structure theorems and applications. International Mathematics Research Notices, no. 19 (2007), 33 pp. (Research paper, in coll. with E. Bombieri and D. Masser; one of the first papers in the theme of the so-called "Unlikely Intersections", now widely studied. Provides in particular a proof of a conjecture of A. Schinzel and B. Zilber.)

On the rational approximations to the powers of an algebraic number:solution of two problems of Mahler and Mendès France
Acta Math. 193 (2004), no. 2, 175-191.
(Research paper, in coll. with P. Corvaja; solves completely two questions of K. Mahler and resp. M. Mendes-France)

On integral points on surfaces. Annals of Mathematics (2) 160 (2004), no. 2, 705-726.
(Research paper, in coll. with P. Corvaja; introduces a new method to study integral points on surfaces, and proves a "Siegel's Theorem for surfaces"; inspired work by several other authors; reproduced by P. Vojta and others in books.)

Finiteness of integral values for the ratio of two linear recurrences, Inventiones Math. 149 (2002), 431-451.
(Research paper, in coll. with P. Corvaja; characterizes the ratios of linear recurrences with infinitely many integral values; provides optimal strong form of "Hadamard-quotient problem", at the basis of a previous weaker conjecture by C. Pisot, solved by Y. Pourchet-A. van der Poorten.)

A proof of Pisot dth root conjecture, Annals of Mathematics, 151 (2000), 375-383.
(Research paper; solves a conjecture of C. Pisot from 50s, concerning perfect powers in recurrent sequences.)
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