Umberto Zannier | Academic Influence

Umberto Zannier's AcademicInfluence.com Rankings

Umberto Zannier

Mathematics

#2582

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#3960

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Algebraic Geometry

#134

World Rank

#141

Historical Rank

Number Theory

#122

World Rank

#161

Historical Rank

Measure Theory

#2863

World Rank

#3404

Historical Rank

mathematics Degrees

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Mathematics

Umberto Zannier's Degrees

PhD Mathematics University of Trieste

Why Is Umberto Zannier Influential?

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According to Wikipedia, Umberto Zannier is an Italian mathematician, specializing in number theory and Diophantine geometry. Education Zannier earned a Laurea degree from University of Pisa and studied at the Scuola Normale Superiore di Pisa with Ph.D. supervised by Enrico Bombieri.

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Umberto Zannier's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Some Problems of Unlikely Intersections in Arithmetic and Geometry (2012) (180)
Intersecting a plane with algebraic subgroups of multiplicative groups (1999) (165)
Rational points in periodic analytic sets and the Manin-Mumford conjecture (2008) (148)
Torsion anomalous points and families of elliptic curves (2008) (106)
Anomalous Subvarieties—Structure Theorems and Applications (2007) (106)
An upper bound for the G.C.D. of an - 1 and bn -1 (2003) (90)
On a general Thue's equation (2004) (88)
Torsion points on families of squares of elliptic curves (2012) (80)
A relative Dobrowolski lower bound over abelian extensions (2000) (72)
Some New Applications of the Subspace Theorem (2002) (72)
A Lower Bound for the Height of a Rational Function at S-unit Points (2003) (72)
On integral points on surfaces (2002) (69)
Diophantine equations with power sums and Universal Hilbert Sets (1998) (69)
Algebraic points on subvarieties of Gmn (1995) (65)
A Note on heights in certain infinite extensions of Q (2013) (60)
On the greatest prime factor of (ab+1)(ac+1) (2002) (60)
An effective “Theorem of André” for CM-points on a plane curve (2012) (51)
A subspace theorem approach to integral points on curves (2002) (50)
The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t) (2003) (49)
Ritt's Second Theorem in arbitrary characteristic. (1993) (49)
Finiteness of integral values for the ratio of two linear recurrences (2002) (48)
Cyclotomic Diophantine problems (Hilbert irreducibility and invariant sets for polynomial maps) (2007) (46)
The class semigroup of orders in number fields (1994) (45)
On unlikely intersections of complex varieties with tori (2008) (43)
Some cases of Vojta’s conjecture on integral points over function fields (2005) (43)
Torsion points on families of products of elliptic curves (2014) (42)
Local-global divisibility of rational points in some commutative algebraic groups (2001) (42)
Genus one curves defined by separated variable polynomials and a polynomial Pell equation (2001) (38)
Fields containing values of algebraic functions (1994) (37)
On the number of terms of a composite polynomial (2007) (36)
On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem (1995) (36)
A uniform relative Dobrowolski's lower bound over abelian extensions (2010) (35)
Some remarks on the S-unit equation in function fields (1993) (35)
On composite lacunary polynomials and the proof of a conjecture of Schinzel (2007) (34)
Lecture Notes on Diophantine Analysis (2014) (34)
Relative Manin–Mumford for Semi-Abelian Surfaces (2013) (34)
On fields with Property (B) (2014) (33)
Heights of algebraic points on subvarieties of abelian varieties (1996) (32)
The Betti map associated to a section of an abelian scheme (2018) (32)
Composite rational functions expressible with few terms (2012) (32)
On the number of integral points on algebraic curves (2003) (32)
On the rational approximations to the powers of an algebraic number: Solution of two problems of Mahler and Mendès France (2004) (31)
Greatest common divisors of $u-1, v-1$ in positive characteristic and rational points on curves over finite fields (2013) (29)
On the Hilbert property and the fundamental group of algebraic varieties (2016) (29)
An analogue for elliptic curves of the Grunwald-Wang example (2004) (29)
On a local‐global principle for the divisibility of a rational point by a positive integer (2007) (28)
Hilbert Irreducibility above algberaic groups (2010) (26)
Integral points on threefolds and other varieties (2009) (24)
On the integral points on certain surfaces (2006) (24)
A Note on Maurin’s Theorem (2010) (23)
A proof of Pisot's dth root conjecture (2000) (23)
On the diophantine equation $f(a^m,y)=b^n$ (2000) (23)
Torsion hypersurfaces on abelian schemes and Betti coordinates (2018) (22)
Finiteness of odd perfect powers with four nonzero binary digits (2013) (21)
On the properties of Northcott and of Narkiewicz for fields of algebraic numbers (2008) (20)
Applications of Diophantine Approximation to Integral Points and Transcendence (2018) (20)
On the integer solutions of exponential equations in function fields (2004) (19)
A Note on squares in arithmetic progressions, II (2002) (19)
Integral points, divisibility between values of polynomials and entire curves on surfaces (2009) (19)
On the reduction modulo p of an absolutely irreducible polynomial f (x, y) (1997) (19)
S-unit points on analytic hypersurfaces (2005) (18)
An effective criterion for periodicity of ℓ-adic continued fractions (2018) (17)
Finiteness results for multiplicatively dependent points on complex curves (2003) (17)
Diophantine equations with linear recurrences An overview of some recent progress (2005) (16)
On fewnomials, integral points and a toric version of Bertini's theorem (2014) (16)
Unlikely Intersections and Pell’s Equations in Polynomials (2013) (16)
On Multiplicative Dependence of Values of Rational Functions and a Generalization of the Northcott Theorem (2017) (16)
Sharpening 'Manin-Mumford' for certain algebraic groups in dimension 2 (2013) (16)
Newton functions generating symmetric fields and irreducibility of Schur polynomials (2009) (16)
On Sums of Roots of Unity (2000) (16)
Products of elementary matrices and non-Euclidean principal ideal domains (2017) (15)
The least admissible value of the parameter in Hilbert's Irreducibility Theorem (1995) (15)
A Lower Bound for Periods of Matrices (2003) (15)
Torsion points, Pell’s equation, and integration in elementary terms (2020) (15)
On recurrent mod p sequences. (1984) (14)
Rational points on Grassmannians and unlikely intersections in tori (2015) (14)
On the torsion values for sections of an elliptic scheme (2019) (14)
Elements of large order on varieties over prime finite fields (2014) (14)
On fields of algebraic numbers with bounded local degrees (2011) (13)
A Note on heights in certain infinite extensions of $\mathbb{Q}$ (2001) (13)
On the length of the continued fraction for values of quotients of power sums (2005) (13)
Multiplicative dependence and bounded height, an example (2000) (13)
Fewnomials and Intersections of Lines with Real Analytic Subgroups in Gmn (2002) (12)
On a functional equation relating a Laurent series f (x) to f (xm) (1998) (12)
On abelian multiplicatively dependent points on a curve in a torus (2017) (12)
Polynomial–exponential equations and Zilber's conjecture (2014) (12)
Universal Hilbert subsets (1998) (11)
Algebraic hyperbolicity of ramified covers of $\mathbb{G}^2_m$ (and integrap points on affine subsets of $\mathbb{P}_2$) (2013) (11)
D-finiteness, rationality, and height (2019) (11)
Addendum to the paper: “On the number of terms of a composite polynomial” (Acta Arith. 127 (2007), 157–167) (2009) (11)
Fields containing values of algebraic functions II (On a conjecture of Schinzel) (1995) (11)
Integral points in two-parameter orbits (2012) (10)
On the linear independence of roots of unity (1989) (10)
Equations in the Hadamard ring of rational functions (2007) (10)
Hyperelliptic continued fractions and generalized Jacobians (2016) (10)
On the distribution of rational points on ramified covers of abelian varieties (2020) (10)
Note on the density constant in the distribution of self-numbers. II (1999) (9)
ON THE INTEGRAL POINTS ON THE COMPLEMENT OF RAMIFICATION-DIVISORS (2005) (9)
BOUNDED HEIGHT IN PENCILS OF FINITELY GENERATED SUBGROUPS (2015) (9)
The group of pythagorean triples in Number fields (1991) (9)
THE DYNAMICAL MORDELL–LANG CONJECTURE FOR ENDOMORPHISMS OF SEMIABELIAN VARIETIES DEFINED OVER FIELDS OF POSITIVE CHARACTERISTIC (2018) (9)
Equations in one variable over function fields (2001) (8)
On the greatest prime factor of Markov pairs (2006) (8)
An $abcd$ theorem over function fields and applications (2011) (8)
Applications of the Subspace Theorem to Certain Diophantine Problems (2008) (8)
On certain permutation groups and sums of two squares (2008) (8)
Non-virtually abelian anisotropic linear groups are not boundedly generated (2021) (8)
LINEAR EQUATIONS WITH UNKNOWNS FROM A MULTIPLICATIVE GROUP IN A FUNCTION FIELD (2004) (8)
Bicyclotomic polynomials and impossible intersections (2013) (8)
On periodic modp sequences andG-functions (1996) (7)
Sums of roots of unity vanishing modulo a prime (2002) (7)
A note on recurrent mod p sequences (1982) (7)
Addendum to "On a general Thue's equation" (2006) (7)
Colloquium De Giorgi 2013 and 2014 (2015) (6)
On a Theorem of J. E. Olson and an Application (Vanishing Sums in Finite Abelianp-Groups) (1997) (6)
Note on dense universal Hilbert sets (1996) (6)
An extremal property of the Möbius function (1989) (6)
Two problems related to the non-vanishing of $L (1, \chi)$ (1998) (5)
On polynomials taking small values at integral arguments II (1983) (5)
Arithmetic properties of certain recurrence sequences (1984) (5)
On Some Applications of Diophantine Approximations (2014) (5)
On the maximal order of a torsion point on a curve in Gnm (2008) (5)
A note on Thue's equation over function fields (1994) (5)
Good reduction of certain covers P1 → P1 (2001) (4)
Diophantine Equations with Linear Recurrences (2018) (4)
Unramified sections of the Legendre scheme and modular forms (2021) (4)
On the $p$-adic distribution of torsion values for a section of an abelian scheme (2019) (4)
Parametrizing over Z integral values of polynomials over Q (2009) (4)
Hilbert's irreducibility theorem and $G$-functions (1997) (4)
A note on traces of differential forms (1999) (4)
Diophantine Approximation and Diophantine Equations (2018) (4)
Remarks on a question of Skolem about the integer solutions of x₁x₂ - x₃x₄ = 1 (1996) (4)
On the number of rational points on certain elliptic curves (2004) (4)
Cyclotomic and abelian points in backward orbits of rational functions (2022) (3)
Solution of a Problem about Symmetric Functions (2003) (3)
Parametrizing Over ℤ Integral Values of Polynomials Over ℚ (2009) (3)
Number Theory: Fields containing values of algebraic functions and related questions (1996) (3)
Remarks on a question of Skolem about the integer solutions of x 1 x 2 − x 3 x (2006) (3)
Remarks on a question of Skolem about the integer solutions of x 1 x 2 − x 3 x (2006) (3)
Generic solutions of polynomial exponential equations (2014) (3)
Values of rational functions on non-hilbertian fields and a question of Weissauer (1998) (3)
On a theorem of Birch concerning sums of distinct integers taken from certain sequences (1989) (3)
Parametrizing SL₂(ℤ) and a question of Skolem (2003) (3)
On the Number of Times a Root off(n, x)=0 Generates a Field Containing a Given Number Field (1998) (3)
Intersections in subvarieties of $G_m^l$ and applications to lacunary polynomials (2021) (3)
Polynomial squares of the form $aX^m+b(1-X)^n+c$ (2004) (3)
Finite Orbits in Surfaces with a Double Elliptic Fibration and Torsion Values of Sections (2023) (2)
Distribution of solutions of diophantine equations $f_1(x_1)f_2(x_2) = f_3(x_3)$, where $f_i$ are polynomials. - II (1994) (2)
Colloquium De Giorgi 2009 (2006) (2)
On periodic mod p sequences (1982) (2)
Integral points on curves: Siegel's theorem after Siegel's proof (2014) (2)
Analytic and rational sections of relative semi-abelian varieties (2020) (2)
Some remarks concerning the rank of mapping tori and ascending HNN-extensions of abelian groups (2012) (2)
Distribution of solutions of diophantine equations f1(x1)f2(x2) = f3(x3), where fi are polynomials (2018) (2)
A variant of the Mordell–Lang conjecture (2018) (2)
AN Ω RESULT IN UNIFORM DISTRIBUTION THEORY (1987) (2)
On the number of terms of a power of a polynomial (2009) (2)
Diophantine Approximation: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, June 28 - July 6, 2000 (2003) (2)
On the rank of certain matrices (2011) (2)
On the distribution of self-numbers (1982) (1)
Hilbert's irreducibility theorem for abelian varieties (2020) (1)
Rational angles in plane lattices (2020) (1)
Introductory Notes on Valuation Rings and Function Fields in One Variable (2014) (1)
On sums of distinct integers belonging to certain sequences (1983) (1)
The Betti map associated to a section of an abelian scheme (2020) (1)
D-finiteness, rationality, and height II: Lower bounds over a set of positive density (2022) (1)
On the Integral Points on Certain Algebraic Varieties (2005) (1)
Acknowledgement of priority (1992) (1)
Composite factors of binomials and linear systems in roots of unity (2019) (1)
Fibred algebraic surfaces and commutators in the Symplectic group (2019) (1)
Bounded height conjecture for function fields (2015) (1)
Finiteness theorems on elliptical billiards and a variant of the Dynamical Mordell-Lang Conjecture (2021) (1)
PENCILS OF NORM FORM EQUATIONS AND A CONJECTURE OF THOMAS (2021) (1)
Diophantine geometry : proceedings (2007) (1)
The Diophantine equation ₁^{₁}\cdots_{}^{_{}}=(₁,…,_{}). II (2009) (1)
Bounded Generation by semi-simple elements: quantitative results (2022) (1)
Integral points on curves f(X)-f(Y)X-Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{f(X)-f(Y)}{X-Y}$$\end{docu (2022) (1)
Addendum to "Some cases of Vojta's conjecture on Integral Points Over Function Fields", Journal Alg. Geometry, Vol. 17, 295-333, 2008 (2010) (1)
Basics on the theory of heights and its applications to certain diophantine problems (2017) (1)
AN EFFECTIVE CRITERION FOR PERIODICITY OF (cid:96) -ADIC CONTINUED FRACTIONS (2018) (0)
REL LEAVES OF THE ARNOUX-YOCCOZ SURFACES W. PATRICK HOOPER AND BARAK WEISS, WITH AN APPENDIX BY LIOR BARY-SOROKER, MARK SHUSTERMAN, AND UMBERTO ZANNIER (2017) (0)
On the integral values of a curious recurrence (2014) (0)
On a Property of the Adele Ring of the Rationals (2004) (0)
U. Zannier ON THE HILBERT IRREDUCIBILITY THEOREM (2009) (0)
Polynomial Squares of the Form aX m 1 b ( 1 2 X ) (2005) (0)
Heights on subvarieties of Gmn (2014) (0)
On the length of continued fractions for values of quotients of power sums (2004) (0)
A note on the zeroes of the Fredholm series (2020) (0)
Number theory. — Rational points in periodic analytic sets and the Manin–Mumford conjecture, by JONATHAN PILA and UMBERTO ZANNIER, communicated by U. Zannier (2008) (0)
Note on g-Hilbertian fields and nonrational curves¶with the Hilbert property (1998) (0)
Chapter 2: An Arithmetical Analogue (2012) (0)
Non-virtually abelian anisotropic linear groups are not boundedly generated (2021) (0)
Unlikely intersections and multiple roots of sparse polynomials (2017) (0)
Thue’s equations and rational approximations (2014) (0)
ON THE BETTI MAP ASSOCIATED TO ABELIAN LOGARITHMS (2019) (0)
Chapter 3 Unlikely Intersections in Elliptic Surfaces and Problems of Masser (2012) (0)
Around the Chevalley–Weil theorem (2021) (0)
On the Hilbert property and the fundamental group of algebraic varieties (2016) (0)
Chapter 4: About the André-Oort Conjecture (2012) (0)
Colloquium De Giorgi 2007 and 2008 (2009) (0)
The diophantine equation $\alpha^{x_1}_1\dots\alpha^{x_n}_n=f(x_1,\dots,x_n)$. II. (2010) (0)
Torsion hypersurfaces on abelian schemes and Betti coordinates (2017) (0)
Value-sets of polynomials at p-adic integers (2012) (0)
Irrationality measures for cubic irrationals whose conjugates lie on a curve (2021) (0)
Composite factors of binomials and linear systems in roots of unity (2019) (0)
An effective solution of a certain diophantine problem (1995) (0)
Basic notions on function fields of one variable (2014) (0)
On the Hasse principle for the division of points in a commutative algebraic group (**) (2005) (0)
On the existence of covers of $\mathbb P_1$ associated to certain permutations (2018) (0)
Arithmetic properties of quadratic exponential polynomials (2019) (0)
Fractional parts of Linear polynomials and an application to hypergeometric functions (2001) (0)
Addendum to the papers "On polynomials taking small values at integral arguments I, II" (Acta Arith. 42 (1983), 189-196; ibid. 106 (2003), 115-121) (2011) (0)
The S-unit equation (2014) (0)
Betti maps, Pell equations in polynomials and almost-Belyi maps (2021) (0)
Heights and diophantine equations over number fields (2014) (0)
Introduction: An Overview of Some Problems of Unlikely Intersections (2012) (0)
The Diophantine equation $\alpha _{1}^{x_{1}}\cdots \alpha _{n}^{x_{n}} = f(x_{1},\dots ,x_{n})$. II (2009) (0)
Points near real algebraic sets (2014) (0)
Some classical diophantine examples (2014) (0)
Colloquium De Giorgi 2010–2012 (2013) (0)
Appendix A: Distribution of Rational Points on Subanalytic Surfaces (2012) (0)
Classification of rational angles in plane lattices (2020) (0)
On cyclotomic multiplicatively dependent points on a curve in a torus (2017) (0)
Chapter 1: Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture (2012) (0)
Elementary Problems: E3457-E3462 (1991) (0)
On some norm form equations (2020) (0)
Artin-Whaples approximations of bounded degree in algebraic varieties (2014) (0)
Torsion points on families of squares of elliptic curves (2011) (0)
Notation and Conventions (2012) (0)
Value-sets of polynomials at p-adic integers (2011) (0)
Integral distances from (two) lattice points (2021) (0)
Introduction Generalities on algebraic functions of one variabile (2014) (0)

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