Umberto Zannier

Geometry and Topology · 2000–2018

A researcher in the Science corpus: 23 papers; trusts 9 researchers and is trusted by 22 researchers here, as inferred from the citation graph.

Subfields

• Geometry and Topology — 39 citations into it; #541 of 7,422 by trust here, #483 by citations
• Algebra and Number Theory — 18 citations into it; #275 of 2,864 by trust here, #222 by citations
• Computational Theory and Mathematics — 15 citations into it; #1,164 of 12,182 by trust here, #1,700 by citations
• Mathematical Physics — 11 citations into it; #3,648 of 8,562 by trust here, #3,664 by citations
• Computational Mechanics — 6 citations into it

Whom Umberto Zannier trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Jonathan Pila
2. Pietro Corvaja
3. Jan-Hendrik Evertse
4. D. Masser
5. Jean-Pierre Serre
6. Andrzej Schinzel
7. C. Smyth
8. Yann Bugeaud
9. Enrico Bombieri
10. Roberto Ferretti

Who trusts Umberto Zannier overall

1. Jonathan Pila
2. P. Habegger
3. Aaron Levin
4. D. Masser
5. Ziyang Gao
6. Pietro Corvaja
7. V. Dimitrov
8. Joseph H. Silverman
9. Fabrizio Barroero
10. Boris Adamczewski

Papers from Umberto Zannier's perspective

Ordered by how strongly the researchers Umberto Zannier trusts endorse each paper. Same corpus, a different order for every researcher.

1. A quantitative version of the Absolute Subspace Theorem
2. A Combination of the Conjectures of Mordell-Lang and André-Oort
3. A Lower Bound for the Height of a Rational Function at S-unit Points
4. An upper bound for the G.C.D. of an - 1 and bn -1
5. Cyclotomic points on curves
6. Real Analysis
7. Towards the Andr\'e-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points
8. Poncelet Polygons and the Painleve Equations
9. Chabauty methods and covering techniques applied to generalized Fermat equations
10. Integer points on the dilation of a subanalytic surface

Their papers

• Rational points in periodic analytic sets and the Manin-Mumford conjecture (2008) — 174 citations
• Torsion anomalous points and families of elliptic curves (2008) — 126 citations
• Some Problems of Unlikely Intersections in Arithmetic and Geometry (2012) — 228 citations
• An upper bound for the G.C.D. of an - 1 and bn -1 (2003) — 108 citations
• Torsion points on families of squares of elliptic curves (2012) — 100 citations
• On a general Thue's equation (2004) — 103 citations
• The Betti map associated to a section of an abelian scheme (2018) — 50 citations
• On the Hilbert property and the fundamental group of algebraic varieties (2016) — 48 citations
• Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn) (2015) — 48 citations
• Torsion points on families of products of elliptic curves (2014) — 53 citations
• On fields with the Property (B) (2014) — 47 citations
• On unlikely intersections of complex varieties with tori (2008) — 53 citations
• Anomalous Subvarieties—Structure Theorems and Applications (2007) — 124 citations
• Cyclotomic Diophantine problems (Hilbert irreducibility and invariant sets for polynomial maps) (2007) — 50 citations
• Some cases of Vojta’s conjecture on integral points over function fields (2005) — 52 citations
• A Lower Bound for the Height of a Rational Function at S-unit Points (2003) — 83 citations
• The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t) (2003) — 54 citations
• On integral points on surfaces (2002) — 84 citations
• Finiteness of integral values for the ratio of two linear recurrences (2002) — 56 citations
• A subspace theorem approach to integral points on curves (2002) — 60 citations